You're right about radiative cooling - I didn't consider that radiative cooling would be that much easier.
I asked claude.ai a bunch of questions.below According to it, purely radiative cooling of a device in space (40-60C) is roughly as effective as very crude conductive cooling of a similar device on earth (internal temp 49 C).
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Consider a 1 m radius spherical object in LEO. One direction, bathed in direct sunlight is coated with solar panels. The electricity generated runs computers internally - the computers are capable of running regardless of the internal temperature of the enclosure. The reverse side is exposed to the 2.7 K of the CMB and had small metal radiative panels.
Compare it to another similar size sphere stored in a room at a constant 22C on earth. Instead of solar panels, the same amount of electricity is pumped in.
In which case would the internal temperature of the sphere be higher?
Make a few assumptions about the other parameters. All power generated by the solar panels in space, or fed in by power lines on earth is immediately used for computation.
Give me rough internal temperatures for both cases
Now assume the sphere on earth is (a) suspended on a thread (b) half buried (c) fully buried , and it has a metal body.
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Answers from Clause.ai
LEO. 40-60 C
Earth.a 95 C
Earth.b 75 C
Earth.c 49 C