It's even better than that. In addition to the factor of n from ratio of volume to surface area, there's also a factor of n from the increased thermal resistance of the mass of the storage volume (the temperature gradient from the surface to the center goes as 1/n). So, the thermal time constant of the object scales as n^2.
This very favorable scaling is why natural geothermal retains heat even though the input energy was delivered gradually over as much as millions of years.
This very favorable scaling is why natural geothermal retains heat even though the input energy was delivered gradually over as much as millions of years.