Geological activity is usually a problem for geothermal cooling. Conductivity of lunar subsurface is your main problem. Generally what makes geothermal really effective is the monstrous thermal mass of solid and liquid material compared to air as well as it's much higher conductivity. While that is true on Earth, on the Moon things are very different.
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.
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.