[kalleboo]

> I assume if one were charging a batter one could also divert some power to keep it warm

The Tesla is always diverting power to keep the batteries warm in the winter. In fact, if you park it outdoors in freezing temperatures, and plug it in to an American single-phase 120V outlet using a long extension cord, all the power will go to keeping the batteries from freezing and it won't charge at all.

[Gibbon1]

Kinda conundrum there, you want good thermal coupling to the environment to shed heat when the batteries are charging. When the car is sitting in the cold you want the batteries insulated.

[stuaxo]

Perhaps bits of metal that can physically touch between the outside and inside (or not) as needed could help ?