Heat is fairly trivially stored for months on a mass scale, check out Polar-night Energy's system - basically, you heat up (usually with just resistive heating) a bunch of sand in a 40metre-wide insulated cylinder, and when you want to use that heat you use fans to blow air through ducts that are surrounded by the sand.

The amazing thing is that every single part of the tech is old and boring - resistive heating is literally as old as electricity, electric fans and ducting are trivial, heating sand is basically impossible to screw up, etc etc.