Some cars, and I thought it was only older cars, have gauges with two coils, where one coil is in series with the thermistor, and the other is between the supply and ground. The needle movement depends on the ratio of current in these coils, so if the battery voltage increases, both coil current increase together and you don't get much change in needle position.
It seems that it would be easiest to measure the voltage on the thermistor, with everything connected as normal, at various temperatures and battery voltages. You can probably just measure with and without the engine running to get around 14.5 V and 12,5 V supplies.