Heat storage has an aspect that was counterintuitive to me, but follows from basic geometry. It benefits greatly from large scale, since the ratio of the volume to surface area [1] decreases the larger you make a container. Accordingly, if a heat tank is large enough, the surface area becomes negligible relative to its volume, and it, in effect, becomes well-insulated by its own mass. For really big tanks, like might…
Gravity seems much more natural to me than heat; eg pumping water up a dam and releasing it again when you need the energy. It strikes me that heat has the problem that it always loses energy in its “stable state” because the surrounding environment absorbs the heat, and gravity doesn’t have this problem.
Heat sinks meanwhile can be built wherever you have a big rock by drilling some holes. Additionally, gravity definitely does lose stored energy in its "stable state", through evaporation and water entering the water table. Losses depend on geology and local climate, but it's not negligible.
Not to say that pumped hydro is a bad technology, it's just got it's own challenges and uses. It's most applicable in the form of electrical grid storage. But specifically on the scale of keeping towns and cities warm, heatsinks outperform almost across the board.