Comment by Xylakant

This exists, in german it's called Eisspeicherheizung. You have a few cubic meters of water buried in a concrete bunker and you use a heat pump to pull energy out of the water until it freezes. The system not only uses the thermal mass of the water, but the thawing/freezing energy which is higher than the energy required to heat water by 1degree by a factor of 80 - meaning if you freeze 1kg of water, you need to pull out enough energy to heat one kg of water by 80 degrees.

You can then use a heat pump that's optimized for the expected temperature range and you don't even need to insulate your water storage tank - you actually want the cold in winter to seep out into the surrounding soil, free energy.

In summer you have cold storage for your AC.