If you have a low thermal mass tip and, most important, with high thermal resistance from the thermocouple to the tip (like a J type), on a big pad you will have much lower temperature at the tip than at the thermocouple, a 4mm D or C tips in a small pad will have much lower errors from this, as the thermal resistance from thermocouple to tip is much lower, think it as a resistive divider from ambient (the pad) to the tip and from the tip to the thermocouple, if you want 320ºC at the tip and you have a low thermal resistance from tip to ambient (big pad) and a big thermal resistance from tip to thermocouple (J type tip) you have much lower temp than expected at the tip. I'm not saying you are going to solder a huge ground plane with a J type, big and small are relative to the tip size, but sometimes you can't get in there with a 3mm tip, you need a 0.8mm tip and you are screwed.
A mathematical model using the thermocouple reading and the applied power will allow you to correct for that error, allowing the thermocouple to read 350ºC when you have 320º at the tip and as the set temp. This could lead to overshoot once you remove the tip from the pad, but to be much more responsive and precise keeping the temperature while at the pad.
JS
PS, here is a VID explaining this with images and measurements... I found it some time ago, I expected to see exactly what he talks about, it's not rocket science but actually doing it right might have some traps. I would expend quite some time in the code if I were to do something like this, if you use the model and you just trust that you could end up pumping way too much power, so I would trust in the model up to a limit and then let the tip go colder than it should when it just can't keep it, so let's say on my example, with a 320º set temp, I would go to 350º at the thermocouple if needed but wouldn't let it go to 400ºC if it reads it needs to do so. It might also be a way to smartly detect a few pre-set different tips, like measuring the initial heating rate, so the soldering iron recognizes what tip you are using. If you use two very similar ones it might get confused but it might not care if the models are close enough. Also, the dispersion between the resistance of different heater element might help to pick the right one too.
https://www.youtube.com/watch?v=EP_Ff2YvkSA&t=0s&list=WL&index=55&frags=pl%2Cwn