If you had watched the video it describes at the 19 minute mark that the yellow wire is required in order to charge the battery. It requires 10k resistance. Blame Logitech.
Oops. I am sorry for leaving this out.
If the yellow wire is for thermistor, yes, it has to be show "safe" for the battery to charge. This depends on the thermistor that was used and how it was connected. What I meant is that this doesn't have anything to do with "knowing when the battery is fully charged" or not.
2 for charging (red and black) and one [yellow wire] for telling when the battery is fully charged or not (yellow) and changing an LED color from red to green.
Putting the yellow wire on a pullup/down resistor is just spoofing the sensor to make it think that the voltage it is reading corresponds to a temp that is under the cutoff. The way the charge circuit knows when the battery is charged (and when to change the LED) is by measuring charge voltage and current (which is going thru the same red/black wires which it is using to charge the battery). *
In the original circuit, Logitech did not design the yellow wire to be connected to a 10K pullup resistor. (Or w/e this guy connects it to.... I'm not going to watch the video). It is connected to a thermistor on the battery, itself, which acts as a temp sensor. And there's a comparator or a logic circuit/micro which shuts down the charging if the thermistor indicates that temp has exceeded a safe limit.
What I meant was you can safely ignore it in the sense that you do not need it to be connected to an actual thermistor reading an actual temp in this scenario, due to the reasons I explained in my last post. You can connect it to a dumb voltage and not worry as long as you are using a battery with a much larger discharge/charge rate (and higher mass/heatsinking). You are BYPASSING a safety feature which Logitech deemed necessary (and indeed may be). When you bypass a safety feature, you should know what you are doing and why. I don't aim to be condescending; if I am using fancy language to repeat something you already know, let's pretend it is for clarity because it is unclear to me that you know what I do. I've been using li ion batteries since the only response you'd ever get from a post like yours (in forums LIKE this, before this one existed) was essentially "don't do it." The only way I learned to use li ion batteries was from ignoring other peoples' advice, ignoring "battery university" website, and actually reading and understanding battery charge IC datasheets; and these datasheets have all the information you ever need to know if you can decify the technical language.
Going larger in the battery takes care of 99% of potential issues with heat while charging. Lower internal resistance means it will handle the max charge rate that the headset can give it without flirting with danger. But you should be aware that if you let the battery go completely flat and don't charge it for a long time, letting the voltage go much below 2.7V, bypassing the thermistor could result in a poof/fire. I suppose this could be a Michael Jackson Pepsi commercial type of problem. A smart charger would charge the battery with a small current until it goes back somewhere north of about 3V. But not all devices will have a smart charger, and in this case the thermistor safety circuit could have been handy. The internal resistance of a li ion battery also goes up over time, so using a battery that is barely beefy enough might result in a problem down the line.
I am not sure what the multiple "-" tabs are for on your battery. If the voltage readings are not the same, they are not redundant ground terminals. Looking at the circuitry on the other side (whatever they connect to) might give a clue.
*Now, in the old days of NiMh batteries, a sharp rise in temp WAS, indeed, how the charge circuit knew when the battery was full. Li ion are much, much more predictable. Float voltage (or charge voltage plus current < arbitrary cutoff point) is all you need to know.
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