From the math I looked at, that doesn’t seem to be the case. What we’re actually doing is fighting radiative and convective heat loss, basically requiring more energy per second to compensate for increasing heat losses per second. An adequately insulted sand battery would negate a lot of that.
You’re right about rapid transfer out. I guess I wasn’t clear about the imagined scenario where the battery may sit untapped for hours or more, and that could definitely cause issues with the metal melting at the upper end of operator temps. Interesting idea for solarpunk story conflict: for whatever reason heat isn’t being extracted fast enough so the batteries are overheating and ‘slagging’ themselves.