Thermocouples are of various types basically differing in the material of construction (e.g. J K R S T B E N). Tables are available for mV vs. temperature. Since the range of mV is way below 100, considerable amplification is required for bringing it into voltage level for ADC’s.
Key problem is Cold-Junction-Compensation. According to the phenomenon, the thermocouple gives zero mV at ambient. Actually a thermocouple measurement is a mV generated between two junctions of differential temperature.
Normal measurements don’t have a ready cold junction. That is why the ambient temperature needs to be corrected. However, note that the temperature of the cold-junction should not be digitally added to the measurement junction temperature. What is required is to generate a mV value equivalent to the ambient temperature, add it to the mV of the measurement junction and then calculate the temperature from the resultant mV.
Using a look-up table is convenient rather than using a best fit curve.