you have a planet you could vent heat into?

Venting heat _into the ground_ is not even remotely an efficient process, unless you have no other option.

Not on earth, where the ground is relatively warm... but lunar subsurface temperatures are -20 or -30°C. You could sink heat into that pretty fast.

They are -20C until you drop a bunch of heat into them. Air works well because it's a fluid. And even as a fluid it's completely ineffective at cooling a cpu. You need to pair that fluid with a heatsink that creates massive surface area and a powered fan that is blowing in a steady stream of cool air to replace the air that has heated up.

Even liquid cooling setups on earth eventually blow their heat into the atmosphere as the primary means of keeping the liquid cool.

Lots of types of rock have better thermal conductivity than water or air. The subsurface of the moon is vast and would dissipate the heat far too quickly for an appreciable temperature change.

But the subsurface of the moon is somewhat less mobile than air or water in cooling systems.

Planet rock is actually a decent insulator in large volumes/long timescales. You’d just heat up the nearby rock quickly, assuming you plan to compute for longer than a week.

https://en.wikipedia.org/wiki/Seasonal_thermal_energy_storag...

Then I guess we'd need to build roving datacentres :)