Assuming it really is raw sensor data (ie 14 bit ADC readings) then rather than knowing how the sensor is tuned you simply ...
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....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