Isn't the moon geologically dead though - no water or geological movements?
I worry this would just result in the ground absorbing the waste heat and eventually becoming too warm to effectively cool anything. Especially because the ground itself would eventually still be limited by the rate of radiative cooling into space, right?
Obviously things like the diffusivity (so conductivity, mass, density etc) of the ground matter a lot, as does the rate of heat exchange at the surface for it to reject (or absorb) heat to the environment.
The problem isn't so much geological activity or lack thereof, as the nature of lunar regolith. Lunar regolith has a conductivity of 0.004W/mK. That is lower than aerogel! So unless the subsurface has a much higher conductivity, using subsurface cooling would be doomed.
Edit: Lunar Regolith is only the first 4-5 meters of the lunar surface.