Assuming it really is raw sensor data (ie 14 bit ADC readings) then rather than knowing how the sensor is tuned you simply ...
....need the raw data that would be used for a standard manufacturer calibration.
The temperatures do not matter much, but using the usual quoted ones you need 3 frames:
Data (20°C flat scene)
Data (35°C flat scene)
Data (real scene)
Then simply crunch the numbers for each pixel for which ImageJ 'image calculations' or even a spreadsheet will do.
Typical ImageJ screens attached, from an ASi sensor, for the first step of (scene - 20°C flat) which is a remarkably credible image given there is no gain correction in there at all.
You then convert to temperature by multiplying each pixel value by its' corresponding [35 flat - 20 flat]/15 and add 20.
That works OK for around ambient, for further away you need to realise that the calibration is in terms of 'energy of a temperature of' not actual °C, so you need to correct for Planck curve effects or get very silly values once going much over 100°C.
Bill