I think you may be overestimating how quickly this happens and underestimating how much surface area that rock has. Given no atmosphere, the fact that the rock with 1/4 the radius of Earth has a temperature differential of only 300C between the hot side and the cold side, there's not a lot of radiation happening.

In deep space (no incident power) you need roughly 2000 sq meters of surface area per megawatt if you want to keep it at 40C. That would mean your 100 MW deep space datacenter (a small datacenter by AI standards) needs 200000 sq meters of surface area to dissipate your heat. That is a flat panel that has a side length of 300 meters (you radiate on both sides).

Unfortunately, you also need to get that power from the sun, and that will take a square with a 500 meter side length. That solar panel is only about 30% efficient, so it needs a heatsink for the 70% of incident power that becomes heat. That heatsink is another radiator. It turns out, we need to radiate a total of ~350 MW of heat to compute with 100 MW, giving a total heatsink side length of a bit under 600 meters.

All in, separate from the computers and assuming no losses from there, you need a 500x500 meter solar panel and a 600x600 meter radiator just for power and heat management on a relatively small compute cluster.

This sounds small compared to things built on Earth, but it's huge compared to anything that has been sent to space before. The ISS is about 100 meters across and about 30 meters wide for comparison.

First, thanks for your knowledgeable input.

Second, are you saying that we basically need to have a radiator as big (approximately) as the solar panels?

That is a lot, but it does sound manageable, in the sense that it approximately doubles what we require anyway for power.

So, not saying that it’s easy or feasible, but saying that cooling then seems “just” as difficult as power, not insurmountably more difficult. (Note that the article lists cooling, radiation, latency, and launch costs as known hard problems, but not power.)

What do you think about droplet radiators? E.g. using a ferrofluid with magnetic containment for capture and enough spare on board to last five years of loss due to occasional splashes?

> 2000 sq meters of surface area per megawatt if you want to keep it at 40C

What is this figure based on?

> it's huge compared to anything that has been sent to space before

That is the goal of Starship though. The ISS has a mass of 400 ton, the goal is to need only two cheap launches of Starship v4 for that.