Semiconductors often specify thermal resistance from case to the junction, but LFP battery cells do not seem to specify this. Instead, they refer only to a generic 'maximum operating temperature'. Since manufacturers don't seem to respond to the question, does anyone have any insight on how to calculate the cell's internal temperature based on case temperature and power output?
The concept of "thermal resistance" with regard to "power output" assumes Joule heat dissipation in one area (junction or resistive element), and heat transfer across the surface of a device. In battery cells the major process is electro-chemical transformation, not resistive heat dissipation.
Consider a Li-ion cell under charge. Say, the charger produces 1 A of current, and the battery is under 4 V level. You have 4 W of electricity flowing in, but the cell remains COLD, because the entire energy transforms into electro-chemical potential. The only heat production comes from the parasitic internal resistance, which is about 100 mOhms (on large signals), so the heat dissipation is just 100 mW, which is negligible for the typical cell geometry/size. That's why the Li-ion batteries stay cool, and start overheating only when there is a problem with chemical process.
The same parasitic dissipation happens on the way of battery discharge - the heat is generated mostly on parasitic resistance. And this parasitic resistance changes over time as the battery ages.
Therefore, the cell temperature can't be calculated solely on "power output", and mostly depends on variable over time parameter - internal resistance (with some chemistry likely involved). I think this is the reason why manufacturers can't and won't specify the thermal resistance of battery cells.
Probably because cells do not have a core junction, rather the whole guts of the battery, which is just under the shell, is what you need to keep below that maximum temperature.
Semiconductors on the other hand you want to keep the actual die below it's failure temperature. The die itself will be significantly warmer than the surface of the casing.
In a cell, casing thickness to guts thickness ratio is small. In semiconductors the opposite is true, the die is generally tiny compared to the packaging.