The basic idea is that the thermal time constant of a uniform sphere (or other shape of fixed aspect) is proportional to the square of its radius. So, for a sufficiently large sphere, the time constant can become very long, >> 1 year. Rock is a good choice because it's very cheap.

The other thing one can do is store cold. This is useful not only for cooling, but for increasing the efficiency of storage of work, since one can generate heat and cold via a heat pump, then reverse that cycle to recover the work. An efficiency of 65% or so may be reasonably achievable with the high temperature in the temperature range of ordinary steel.