[onetimeuse92304]

> I cannot explain the physics

Here, this is actually the problem.

Water can store many times the amount of energy per volume or mass, per degree Celcius, than rock.

What you see is that rock has much lower thermal conductivity. It can be hot inside but it is not as good at transferring that heat outside. It means when you have hot rock it will stay hot for longer than equivalent amount of water. That because water emits that energy faster.

But put that rock and water in a well insulated vessel and you will find that the properties of the insulation and the vessel will start dominating the process and what counts now is how much energy you can store in the material inside.