Storing heat for months requires really, really good insulation, and insulating many small stores is far more expensive than insulating one big store (essentially a square-cube thing).

So this kind of thing may only be viable for industrial processes.

In the residential context, the magic word here is "ground source heat pump". A really big coolant loop that stores heat underground. Depending on the jurisdiction and loop size, figure it will cost $15,000+

Sounds great!

I wonder: Why is sand better than the dirt that’s already on site? Dirt, after all, contains water, which I believe should have an even higher thermal capacity, or not?

Also: How about combining this approach with a heat pump instead of resistive heating?