HVAC engineer here. At the residential level this is already achievable with hot water storage from either solar thermal and/or heat pumps. Plus you get to use the hot water (assuming you've sized the tank correctly!)
Storing heat in rocks or sand doesn't make sense from a thermal efficiency standpoint unless the temperature is high and that isn't economically viable unless you have large volume storage - typically district or precinct level.
Storing heat in rocks or sand doesn't make sense from a thermal efficiency standpoint unless the temperature is high and that isn't economically viable unless you have large volume storage - typically district or precinct level.