V battery and T battery while charging

[RoGeorge]

Bought two sets of 4 NiMH rechargeable AA batteries this weekend.  The box says fabricated 2024-06.  Brand Tronic color (from LIDL), ready to use (charged), NiMH, 1.2V, 2500mAh, but the nominal 2500mAh will be reached only after the first 5 cycles or so.  Which raised the question of how many mAh will they show during these first 5 dis/re-charging cycles.

At the 1st discharging, found the shelf charge to be about 1770..1780mAh.

Then it was the time to recharge them for the first time.  On the battery body is written to charge at 500mA for 7 hours, which I did with a DP832 lab power supply set as a 500mA constant current and no more than 10V, to charge 4 of 1.2V in series at once.  Since the DP832 has SCPI, also logged the battery voltage during the charging, one sample every 10 seconds.

Decided to log not only the battery voltage during these 7 hours of charging, but to log the battery temperature, too, with an additionally DMM and a K thermocouple probe placed in the middle of the 4 batteries pack.



I knew the temperature is expected to raise, particularly after the battery became fully charged, because once the battery is full, most of the input energy will turn into heat, but never logged the temperature before, and I was expecting to see a slowly raising temperature during the entire process with some temperature gain at the end.

However, it was a surprise for me to see an almost constant temperature during the entire charging, and with a big jump in temperature at the end, after the batteries became fully charged. 



I've read the detection of negative delta V (as a charging termination criteria) can be tricky to detect in wear-out batteries, particularly when charging each individual cell.  Most of the chargers I have do not measure the temperature at all, yet the jump in temperature looks very easy to spot. 

I wonder why the delta T is not used more often as an end of charging strategy?

[Benta]

I wonder why the delta T is not used more often as an end of charging strategy?

Because when the temperature begins to rise, you're already overcharging (=damaging) the cells. It is used in very primitive chargers.

[Siwastaja]

I was expecting to see a slowly raising temperature during the entire process with some temperature gain at the end.

However, it was a surprise for me to see an almost constant temperature during the entire charging, and with a big jump in temperature at the end

Yeah. Think about it: if the cell heated up during charging at such low current (C/5), that would indicate very poor efficiency. Yet NiMH was used still recently in hybrid EV battery packs etc.; the efficiency is just fine, even at higher currents. Larger temperature increase would also go hand-in-hand with larger voltage droop under load. And that is something NiMH is known not to do. They have pretty low internal resistance.

So the heating you see is indeed at the end, from the unwanted internal "side reaction", or shunting. This reaction causes loss of charge efficiency (coulombs converted into heat, instead of being stored in a dischargeable form). As Benta points out, it's really unwanted. It really depends on the chemistry specifics how harmful it exactly is, but there is no advantage to overcharging modern NiMH cells as far as I know.

Interesting experiment would be to do charge and discharge tests and integrate coulombs (Ah) in, coulombs out, to calculate coulombic efficiency. Which for things like li-ion which have no safe shunting mechanism at all is like 99.95%. But for NiMH that would heavily depend on how you detect your charge stop point. I'm sure folks like Toyota who used NiMH cells in hybrid vehicles knew this stuff.

[Siwastaja]

It [delta T] is used in very primitive chargers.

On the other hand, take a close look at RoGeorge's graph. Actually positive dT happens already before the negative dV, which is used by the modern chargers. It's just not very fast rise at that point yet. So I think it could be useful, and don't quote me on this, but I think real high-end chargers at least bragged doing both dT and dV detections. In good case, a sensitive and well-coupled dT triggers first, and if not, negative dV triggers next. As last resort, if negative voltage drop is too small, then even insensitive dT finally triggers.

The key for good dT detection would be good thermal coupling to the cell. Which could be difficult when the cells are removed and inserted to the charger by the user. But if you were allowed to use a small piece of sil-pad and tape a thermocouple to it and sense the derivative of the temperature, you could do it better than negative dV alone.

Now using negative second derivative (let's call it -ddV) of the voltage instead, i.e. detecting the point where voltage rise starts to slow down, would be interesting. That seems to happen very close to the temperature starting to increase, and well before the negative dV.

[Benta]

Advanced NiMH/NiCd chargers have been available for years, and the charging scheme/algorithm is proven for maximum life as well as fast charge.
An interesting point: fast charge (1C...2C) will not heat the cells much during the linear voltage region. At room temperature, they'll perhaps be hand-warm, no more. This is from practical experience.

The algorithm is normally:
1: a formation charge at C/20...C/10 for a couple of minutes. This is to establish that the cells are OK, and to find the initial charge point.
2: fast charge at 1C...2C using d²V/dt² cutoff detection. This will detect the upward voltage curve change.
3: at that point, reduce charge current to C/5...C/10 for top-off charging.,, still using d²V/dt² detection to stop charging just before the voltage peak.

dT detection can be added as a safety measure, but is not suitable for charge stop detection.

EDIT: intelligent fast charge (C/2...2C) will let your cells last longer, as dendrite growth is prevented.

[RoGeorge]

About the dV termination, I vaguely remember one was stopping for dV = 0 (top V), the other method was stopping for dV < 0 (descending slope after the top), one for each type of chemistry (Ni-Cd and Ni-MH), but I'm not sure which was for what chemistry type and can not google right now.


About taking damage at overheating, not contesting that, but I'd I've had an interesting charging "accident" last weekend, with some Varta AA NiMH 2100mAh that were bought about 10 years ago.  It was written on them that they support fast charge, so I've put them at 1A for 2 hours, and forgot to disconnect them until I've sensed burnt-like smell.

They were heating so much that the self adhesive underneath the plastic cover unglued and starting to make gas bubbles underneath.  The batteries did not vent, though.  I thought I've killed them, but anyway, disconnected and started to log the voltage after disconnecting them (I was curios for V open vs T battery).

Did some plots that maybe I would post in another topic, but the curios thing was that after letting them to completely cool down for a few hours, I've test their short circuit current, and the I short increased a lot, from about 2A before the overheating accident, to about 5A after that.  Same, the measured mAh increased with about 20% or so after the unintended overheating "treatment".

There is more to measure, and maybe to repeat that with some other brands, but I suspect I might have accidentally found a way to partially rejuvenate the internal resistance of old NiMH batteries. 


Since it came the topic of short current measuring, I've measured that for the new Tronic 2500mAh, too, and I short-circuit (with the DMM probes included, don't know the exact resistance of the DMM probes and contacts) was about 10A for the shelf charge, then 10A then fast decreasing for the same batteries after fully discharging them at 0.2C down to 0.5V.

The attached plots is for all of the 8 new batteries I have, each battery tested for 10 seconds short, then moving the DMM to the next battery, and so on.  One chart is for the shelf-charged batteries, the other after fully discharging them at 0.2C.  Any sudden drops in current during the 10 seconds of continuous short are all my fault, I was pressing the probes too hard and slipping on the + connector.

[Benta]

This is getting silly and anecdotal.
I provided a serious answer, but that seems to have been a mistake.
Have fun.

[RoGeorge]

Not silly, and certainly I was not commenting against what you wrote.  In fact, d''V method you mentioned is the same as dV=0.

My reply was mostly because the remark about overheating (as a bad practice) reminded me about the strange result observed after that heavily-overheating accident.  Anecdotal or not, there are a few hours of logged charging/discharging that can confirm those observations.  After the accident, the max current did increase at least 2x (from 2A to 5A short-circuit), and the C increased with about 10%-20%, too.

As I was already wrote, will have to repeat the overheating experiment on another brand of batteries, to see if the effects are reproducible.

I'm sorry my lab mistake felt out of the template of your serious answers.   
We each bare our own mistakes.  You have fun, too.

[Benta]

All OK, but comixing smashed cells with a discussion on how to do it correctly turned me off a bit.

In fact, d''V method you mentioned is the same as dV=0.

No, it's not.
Detecting dV=0 is the top of the voltage curve, which is far too late (even dT detection would be better than that). And you can't realistically detect dV=0, you can only detect the falling voltage after the peak, which is even later.
d²V/dt² detects the upward swing of the voltage curve, which is the cutoff point for high current charge (and transistion to top-off charge).
And it also detects the flattening out of the voltage curve before peak voltage.

[RoGeorge]

Panasonic stops the fast NiMH charging at negative delta V, downhill after the peak voltage:

∆V value: 5 to 10mV/cell. When the battery
voltage drops from its peak to 5 to 10mV/cell
during rapid charge, rapid charge is stopped, and
the charge method is switched over to trickle
charge.

Quote is from Panasonic NICKEL METAL HYDRIDE HANDBOOK, PAGE 12 AUGUST 2005
https://api.pim.na.industrial.panasonic.com/file_stream/main/fileversion/3486


Other charging methods for NiMH, by Panasonic:

Image from: https://energy.panasonic.com/global/business/e/na/products/nickel-metal


Later edit
------------
Meanwhile found the page where from to download the latest Panasonic Handbook from 2023:
https://industry.panasonic.eu/products/energy-building/batteries/battery-cells/secondary-batteries-rechargeable-batteries/nickel-metal-hydride-batteries

Ni-MH Technical Handbook 2023
https://industry.panasonic.eu/storage/custom-upload/Energy & Building/Batteries/Secondary Batteries/Nickel Metal Hydride Batteries/Panasonic Ni-MH Batteries Handbook.pdf

Catalog (not Ni-MH only)
https://industry.panasonic.eu/storage/custom-upload/Energy & Building/Batteries/Panasonic_Industrial-Batteries-For-Professionals_Short-Form-Catalog.pdf

[Benta]

Interesting chart, thanks! Gives a good overview.
If you look closely, then what they call "Step Charging" is actually the d²V/dt² method and hits 100% charge.
Note also that the other methods overcharge the cells, which is in line with my experience.
d²V/dt² also allows for ultra-fast charge.

[Siwastaja]

Interesting chart, thanks! Gives a good overview.
If you look closely, then what they call "Step Charging" is actually the d²V/dt² method and hits 100% charge.

Yeah, clearly what they call "step charging" implements two completely orthogonal methods: using second derivative instead of first; and lowering charging current (just in a step, not continuously) towards the end.

They don't say this clearly, it needs to be deducted from the picture. To me the "step" thing (two current levels) is less interesting.

I have though using second derivative is some sort of bleeding edge special thing, because you rarely hear about it: all commentary is about -dV/dt versus temperature. But maybe this is the classic echo chamber thing, just like in li-ion discussion we still hear some weird crap that was written on "Battery University" site nearly 20 years ago.

[jwet]

Maxim made zero slope termination (712) and negative delta-V (713) versions of the same charger IC's- ie MAX712 and 713 among others.  Note that this is for fast charge type termination >C/2.   The 712 data sheet go through it very thoroughly and makes a good read.  It released when NiMH was a new chemistry and NiCd was the dominant type in use (Early 90's).   NiCds used negative delta V and NiMH was zero slope but could do either.   Negative delta-V is really an indirect measurement of overcharge/pressure build up but the slope changes were very small.  If you charge a NiCd to zero delta-V, you'll get something like 90% capacity.  Temperature should also be measured for safety. 

[RoGeorge]

The datasheet was a good hint, thanks.
https://www.analog.com/media/en/technical-documentation/data-sheets/MAX712-MAX713.pdf

Found the eval kit pdf, too, with more examples plus this paragraph

Choosing Between the MAX712 and the MAX713

The MAX712 is intended to charge only NiMH batteries
because it uses a zero delta voltage full-charge detection
scheme. The MAX713 can be used to charge either NiCd
or NiMH batteries because its 2.5mV-per-cell resolution
allows it to detect the very slight peak in the NiMH charge
characteristic. Some NiMH batteries require three differ-
ent current levels when charging: an initial high current,
an intermediate topping-off current, and a low trickle cur-
rent. Neither the MAX712 nor the MAX713 is intended to
charge this type of NiMH battery.

https://www.analog.com/media/en/technical-documentation/data-sheets/MAX712EVKIT.pdf

At this point I should write a script for an SCPI charger with my Rigol DP832, or else I'll forget all these details again. 

[tooki]

Here’s some more documents on the topic. The Panasonic one I added because it’s still a version that uses “C” for the charge/discharge rate, rather than “It”/“lt” they changed it to in later revisions for some reason.

(Someone correct me if I’m wrong, but I assume “It” (capital i, lowercase t) is supposed to mean current x time, and that “lt” (lowercase L, lowercase t) is a typo due to someone misreading I as l? )

[Benta]

Interesting chart, thanks! Gives a good overview.
If you look closely, then what they call "Step Charging" is actually the d²V/dt² method and hits 100% charge.

Yeah, clearly what they call "step charging" implements two completely orthogonal methods: using second derivative instead of first; and lowering charging current (just in a step, not continuously) towards the end.

They don't say this clearly, it needs to be deducted from the picture. To me the "step" thing (two current levels) is less interesting.

I have though using second derivative is some sort of bleeding edge special thing, because you rarely hear about it: all commentary is about -dV/dt versus temperature. But maybe this is the classic echo chamber thing, just like in li-ion discussion we still hear some weird crap that was written on "Battery University" site nearly 20 years ago.

I understand your perception. d²V/dt² sounds awfully mathematical and brings pictures of DSPs into mind.
In fact, in can be done with the lowest cost MCU with ADC on the market, and the code is simple.

I first learned of the concept in the mid-90s when Temic (ex Telefunken) brought out a family of NiCd/NiMH charger ICs. Long obsolete and surpassed by cheap MCUs.

But studying the datasheets bring a lot of insight. I attach one here.

The algorithm is actually not d²V/dt², but rather a discrete version: delta²(V)/delta(t²).
It's simply comparing a voltage sample with the previous one by subtraction. That's the delta(V)/delta(t).
When the difference gets too large between samples (that's your delta²(V)/delta(t²)), you stop the fast charge and go to top-off charge.
Top-off charge is stopped using -delta(V)/delta(t).
A better stop criteria would be delta(V)/delta(t) = 0.

[Siwastaja]

I understand your perception. d²V/dt² sounds awfully mathematical and brings pictures of DSPs into mind.
In fact, in can be done with the lowest cost MCU with ADC on the market, and the code is simple.

Of course: you need some tens of Hz of CPU clock rate, and probably some hundreds of bits of memory. You can do it with a relay-based or mechanical computer. A 8-bit PIC is already an overkill. Also possible to do with a few opamps and analog circuitry, but probably much easier to do robustly on an MCU.

Then again, devil is in the details. Measurement noise affects how small thresholds can be used. If charging is slow, then both the amplitude of the voltage peak is smaller, and it happens more slowly, making the derivative term quadratically smaller. Which is why these stopping conditions are only used at relatively high charge currents.

It's simply comparing a voltage sample with the previous one by subtraction. That's the delta(V)/delta(t).
When the difference gets too large between samples (that's your delta²(V)/delta(t²)),

To be clear, this is the first derivative:

Code: [Select]

static float prev_voltage;
float cur_voltage = read_adc();
float dv = cur_voltage - prev_voltage;
if(dv < -10.0)
    ... // This is a -dV/dt detection
prev_voltage = cur_voltage;

Second derivative is this:

Code: [Select]

static float prev_voltage;
static float prev_dv;
float cur_voltage = read_adc();
float dv = cur_voltage - prev_voltage;
if(dv < prev_dv) // can be written explicitly as ddv = dv - prev_dv and comparing it against a threshold
    ... // This is second derivative detection: detecting when the voltage slope starts turning down
prev_dv = dv;
prev_voltage = cur_voltage;

[RoGeorge]

..
d²V/dt² sounds awfully mathematical
...
the datasheets bring a lot of insight. I attach one here.
...

Thanks for the datasheet, not only it explains their procedure, but also gives the numerical values to trigger the termination of fast charge.

The sign of the first derivative tells the slope, in other words, it tells if the original function is increasing or decreasing.  The sign of second derivative tells if a curve is concave or convex.  The intuitive meaning of the first two derivatives is not that awful, just that I didn't know there were chargers looking at the second derivative of V.

Aside from the Maxim and Temic datasheets, I've just read the datasheets of a few more charging ICs from LT and TI.  They are slightly different, both in numerical values and in the exact procedure.  However, they all have in common the warning that, before anything, one should check with the battery manufacturer for the exact recommended recharging method.

Since my pile of batteries is from various manufacturers, and from various periods of time (some as old as 20+ years), I guess I'll just try to compile my own recharging method, by summarizing the values from all those IC charger datasheets. 

Already have many ready-made chargers, just that I'll prefer to use my own charging procedure (with a DP832 PSU), so I can make the measurements reproducible.


Now, philosophical question:
If the label of a battery specifies 1000mAh nominal, but the battery is not new, and now it can only hold 600mAh (measured), do I charge it as if it were a 1000mAh, or do I charge it with the current corresponding to a 600mAh battery? 

[Siwastaja]

Now, philosophical question:
If the label of a battery specifies 1000mAh nominal, but the battery is not new, and now it can only hold 600mAh (measured), do I charge it as if it were a 1000mAh, or do I charge it with the current corresponding to a 600mAh battery? 

If going deep into battery chemistry, I'm sure there will be reasoning for both choices. Therefore, golden middle road: charge it as if it was a 800mAh battery 

[jwet]

Chargers usually don't make this adjustment- they continue to charge as if C was 1000 mAHr.  Besides the capacity going down, the charge efficiency goes down so this keeps the time to charge roughly the same.  Lenovo notebooks at least the higher end models store a lot of battery data and logs.

These advanced fuel gauge things where the capacity of the battery is known from its charge/discharge history are a relatively new innovation for small batteries and apply mostly to LiIon.  Big batteries like on large sailboats etc have fancy fuel gauging systems.  There is a formula called Peukert's law that mostly applies to Lead Acid chemistries.  Google it- Li Ion are similar.

If you're digging in deep, the patents for this stuff can be a good read.  Maxim patented several versions of "Model Gauge" and TI did similar with their "True Gauge".  The Maxim engineer that did most of this work was Jason Wortham, I think he landed at Apple, IIRC- smart dude.    The patents have to give the reader enough to "enable" the invention but will usually leave out some non obvious little tip.

[RoGeorge]

Here's something funny:

A sudden increase in temperature indicates you should stop, no matter that you charge or discharge the battery. 


This is the V and T while discharging the AA NiMH under constant I=500mA.

My guess is the internal resistance suddenly increases when the battery is empty, and since the produced heat is proportional with R, that will eventually raise the temperature more when the battery becomes empty.


Putting aside the discharging temperature, I've measured again the temperature while charging, only this time the charging was made with a Sony fast charger model BCG-34HRMF.  This Sony fast charger pushes 510mA, has delta T and delta V detection, and individual thermistor for each battery.


- Yellow and Orange are from the first charging, V and T cell charging with a PSU at constant 500mA for 7 hours.
- Blue is the temperature of the battery when charged inside the Sony fast charger, at 510mA, with termination at dT and/or dV, followed by some topping/trickle charging.

The temperature was much higher with Sony because the charger has a plastic lid.

Notice that the blue line has 2 slopes after the battery is full, with a knee between the 2 slopes somewhere around 4h:30min, that is where the main charging terminates, then a topping charging continues for about 1 more hour, then the battery slowly cools down towards the room temperature.

Side note, the charger displays full battery at 4:30, not at 5:30.  This looks like a software bug, because the temperature keeps raising in the next hour, which denotes the charger still pushes current for one more hour after the display indicates battery charged.


Because the charging and discharging were made at almost the same 500mA, and because the efficiency was close to 100%, the charging or discharging took about the same 4h:30min.  To compare the temperatures (and time) on the same scale, these are all 3 measurements mixed in one chart:


- Charging w PSU for 7h at 500mA, V and T
- Discharging down to 0.5V at constant 500mA, V and T
- Charging w Sony fast charger, only T was measured, no V

The attached .zip contains the .csv raw measurements and the .gp plotting scrips.

[jwet]

I think Benchmarq (acquired by TI in the mid 90's) had a termination technique that was based on delta T/delta t- time derivative of temp. Bq2003 or similar IIRC.  It's a good thing as a backup termination method but shouldn't be primary in my opinion.  My original specialty in my EE Education was as a control engineer- derivative terms can be included in control equations but should be used mainly for shutdown signals- they generally aren't reliable for forward terms because they are high pass in nature and respond to steps and high frequencies too strongly.  Having a fault mode of high temp rise over time is good but its not a reliable main termination method, it would tend to false trigger creating undercharge.  A gross over temp limit is a requirement but looking at slopes has problems.

[RoGeorge]

Did yesterday another recharge with the Sony charger, this time with the plastic lid removed.  I was expecting to see a much lower temperature during the first hours of main charging, but to my surprise T was about the same. 



Light-blue is T with the plastic lid cover closed, dark-blue is with the plastic lid removed from the charger.  Both dark/light blue show a much higher temperature than the orange line.  (Dark) orange plot is the T while charging with a PSU for 7h at a constant 500mA and no end-charging detection.

Sure, either with the lid on or off, the Sony charger is much smaller, and has less ventilation than my DYI battery holder from when the T with PSU charging and no termination was measured (the orange line).  Showing all 3 arrangements to see the difference.


- DIY battery holder and PSU 500mA for 7h, no termiantion detection (logged T for this setup was plot in orange)


- Sony charger with the plastic cover lid closed (logged T for this setup was plot in light-blue)


- Sony charger with lid removed (logged T for this setup was plot in dark-blue)

Did a zoom-in, to observe better the T around the charging termination:



The point of main charging termination is much clear now (somewhere between 04:30 and 04:45).  Then it's a constant slope, then at the tip is flat, a max temperature limitation I guess, then the topping phase ends and naturally cooling down starts.

Also notice how the second charge, the dark-blue line, ends later than the first charge (light-blue).  I guess this is because a NiMH battery only reaches its nominal C (mAh) after a few cycles of repeated charging/discharging.  These are brand new NiMH, and the light and dark blue are their very first 2 recharging.  The second rechearging takes longer because the mAh of the battery is increasing.  On the battery blister it says nominal 2500mAh is to be expected after 5 complete cycles of discharging/recharging.

The slight increase of C was noticed, too, while discharging the batteries for the first 2 times.  At first discharge they measured about 1780mAh.  At their second discharge, they measured about 2100mAh.


About the main-charging T plateau of blue lines (the plateau during the first 4 hours, not the short flat-top of max T limitation), first hours of a much higher T (with +20*C more relative to the orange line), no mater the cover lid was on or off, I suspect maybe the higher T is because the Sony charger is using PWM instead of DC. Could be less ventilation, but the almost identical T in dark vs light blue plateau (lid cover on/removed) made me think the cause might be Sony is using PWM instead of a constant DC current.  At the same average current, a PWM will produce higher T than the same curent at DC, because the heat is proportional with the square of the current (Q = I²*R*time).

On a second thought, good ventilation is crucial for cooling.  For example, the small T noise seen at the very beginning of the magenta line was because I was cleaning the desk, thus altering the natural convection currents above the workbench.



The much taller spike there is because I've blown hot air on the battery (from the lungs) to check how sensitive the thermocouple probe was to air currents.  Very sensitive, the T spiked immediately.  Then I've stopped cleaning the bench, moved away, and from that point on (00:15) only the quantization noise remained.

Didn't found the time yet to insert a current probe in series with the batteries (to see if Sony uses PWM, or the increased T plateau is caused only by the less natural ventilation).

[Siwastaja]

My guess is the internal resistance suddenly increases when the battery is empty, and since the produced heat is proportional with R, that will eventually raise the temperature more when the battery becomes empty.

Same happens with li-ion: below 20% SoC or so, higher voltage drop (compared to open-circuit voltage), hence higher equivalent R if calculated from dV/dI, and as a result, more heating.

Remember though that heating is not only resistive, the chemical reactions can also store or release energy (enthalpy), distinctive is that in one direction reaction is exothermic and to opposite direction is endothermic; so that if the contribution of "resistive losses" are completely removed, the battery heats up at the end of discharge and then cools down when you start charging it. And at least with li-ion you can actually observe this. It's quite cool to think that the thermal capacity of the battery and the universe where the battery sits contributes then to energy storage; during discharge you lose energy to heating, but during charge you suck this thermal energy back from the battery and its surroundings.

Of course adding the contribution of resistive heating you (usually) would observe heating both ways, but asymmetry in amount of heating would indicate there is more going on than just resistive heating.

[RoGeorge]

My impression so far is that the main contributor to temperature increase during the end of discharging is due to the increase of the internal resistance (but I didn't directly measured the variation of Ri during charging/discharging), while the massive heating at the end of charging is caused by the increase of the internal pressure inside the battery under a constant volume.

Gases are produced during the charging process, most are absorbed by the porous metals inside, until the end of charging when no more gases can be absorbed.  Thus, the internal pressure increases, and since the battery is sealed, being under a constant volume this translates into a higher temperature because pV=nRT (where all the p,V,n,R,T are about gases, https://en.wikipedia.org/wiki/Ideal_gas_law )

Isn't that how it is?

If it were for the temperature variations to be caused mostly by the endothermal/exothermal character of a chemical reaction, then I would expect to see the temperature increasing or decreasing during the entire duration of a charging or a discharging, which in the case of NiMH does not happen.  During the most time, either it is charging or discharging, the temperature doesn't change much.  Only at the end of the process there is a sudden temperature raise, except the cause of the T raise is different for charging vs discharging.  For charging the main cause is an increase in the internal pressure, for discharging the main cause is the increase of the internal resistance.

Can't say for Li-ion, because I never measured Li-ion temperature while charging/discharging, but you made me curious.  I didn't know there could be a temperature decrease with Li-ion.  Will definitely try to measure T for Li-ion, too.