[quantumstate]

"If you need heat, it's much more fuel efficient to just burn fuel and not bother turning it into electricity in an intermediate step."

This isn't always true. Carnot's Theorem works in reverse as well, so you can use a heat pump (like an air con unit) so get more heat out of your electricity than just dumping it into a coil. This is actually practical and is being done today for heating houses, you can easily beat the other inefficiencies because the temperature difference that you are trying to create for your house is much smaller than the one between the gas furnace and the ambient temperature around the power station.

For heating a pan though I think this is unlikely to be practical any time soon.