Apples to oranges, long-lived satellites have modest power needs. Doing a back-of-the napkin math on required size of solar array and radiative elements for a single-rack's worth of energy is a sobering exercise for those who are a overly exuberant on the topic. The all-in power estimate for a single GB300 chip is 2.1kW
Edit: ISS is about 90KW steady state, and the collector to radiator area ratio is about 5:1. Dunno about the mass ratio.
My point is not that space data centers are viable or sensible. Only that the need for cooling is limited. If a terrestrial datacenter was powered only by its rooftop solar panels, cooling it would be trivial. Space is harder, but there just isn’t that much heat to dump.
A simple rock in orbit radiates exactly as much heat as hits it from the sun, on average.
You are correct that the first law of thermodynamics dictates the energy, but anyone who has parked a car in the sun will tell you, the temperature where the absorption/dissipation equilibrium is achieved is often incompatible with the survival of the cargo.
edit to your edit:
> Edit: ISS is about 90KW steady state, and the collector to radiator area ratio is about 5:1. Dunno about the mass ratio.
Cool; that's about half the wattage of one modern full-height Nvidia AI rack (172kW) - you need two ISSes to service just 1 rack; extrapolate that to a data center's worth of racks and see if the math is mathing. The ISS is about the size of a(n American) football field.
You won't immediately freeze if you enter space without a suit. You'll die almost immediately, but it will be because your blood will begin to boil because of the lack of pressure kinda like an extreme form of divers sickness - it's just not the cold that'll get you first.