[Qwertious]

>You just have to replace natural gas with a synthetic fuel.

The word "just" is doing a lot of heavy lifting there. For heating, by far the most sensible solution is to use summer PV to heat up a bunch of sand/rock wrapped in a ton of insulation, then use the stored heat in winter.

[adrianN]

I did not claim that it's the cheapest method, I just pointed out that storing months worth of energy is feasible.