one significant thing I missed when I was writing this up is that stationing a data center on the surface of another celestial body is _slightly_ more reasonable than stationing it in space for the purposes of cooling; you can build a moon base to cool itself by driving a big old copper spike into the ground and running coolant through it.
but you can also do that on earth. people already do[1]. and unlike the surface of the moon, the surface of the earth doesn’t get up to 250F in the middle of the two-week-long day[2]. (yet.)
[1]: https://betterbuildingssolutioncenter.energy.gov/showcase-projects/iron-mountain-data-centers-geothermal-cooling-system
[2]: https://www.space.com/18175-moon-temperature.html