I think the polystyrene box is still worth the experiment; if external conduction can be limited (eg for all the I/O wires) the heat loss may be minimal. Pretty easy to stick a box in a freezer (generally around -20C) and see how much dissipation is required to maintain +20C inside.
There’s also no reason you can’t just wake, check the temperature, and if it’s chilly, stay awake (and maybe spin busy) to warm it up a bit - no need for resistors etc. You don’t need to be transmitting to burn 100mW+. Obviously, this process burns exactly the same amount of battery power as any resistive heater.
As I’m on a plane and thermal boxes have always fascinated me, I thought I’d try and work it out… there now follows some probably incorrect calculations, assumptions, and misuse of units and/or websites, and a conclusion:
ET-369 has an R-value of 23.08 (I’m assuming this is imperial vs SI, hence is in sqft farenheit-hour per BTU… oh my, there’s a unit…)
Internally it’s roughly a foot cube, ie it has 6 square feet of wall area
https://rimstar.org/renewnrg/heat_transfer_loss_calculations.htm with A = -40F (-40C), B = 68F (20C), 6 square feet, R-value of 23.08 says 28.1 BTU/hour heat transfer.
1 BTU/hr is equivalent to 0.293W (ie joules per second)
So to maintain internal temperature with that 60C delta you’d need to be dissipating 8.24W. That seems quite a lot, whether you’re using a resistor to heat or anything else. Aiming for 0C/32F inside instead still needs over 5W constantly.
Ouch. Let’s try a smaller box:
ETM-309, same R-value, but 2.45sqft wall area (8x8x6ish)
Now 3.36W for 60C differential, or 2.23W for 40C.
I think it’s not going to be viable to heat through cold nights for a lithium cell unless you want to make a thick box out of aerogel (or wrap that one in aerogel). It seems much easier to just use a lead-acid battery. Of course, the calculations could be wrong - I’m a little surprised at how much power was required.