I was hoping you might do the analysis. But surface to volume ratio seems important here. if we are storing cities worth of heat then the self insulation of baked soil might be plenty. sketch: dig deep hole, bury big resistor, cook in summer, collect surface heat in winter.

There is a Finnish company heliostorage.com/products/btes/
doing just that, storing heat in the subsoil, but not at elevated temperatures above 100. Not sure how successful the technology is as no recent breakthroughs are reported and the even the site in Drake Landing is now dismantled.