Nobody (sane) is talking about putting nuclear reactors on Satellites in close Earth orbit so we don't have to worry about them generating heat. They've got solar panels that move some of the solar energy they absorb to a central location which presents problems in moving the waste heat back out so that spot doesn't get too hot. But that doesn't change the overall equilibrium temperature.
In the vicinity of the Earth, they get to about the temperature of the Earth. That’s not a coincidence. Hotter if they are actively generating heat.
Nobody (sane) is talking about putting nuclear reactors on Satellites in close Earth orbit so we don't have to worry about them generating heat. They've got solar panels that move some of the solar energy they absorb to a central location which presents problems in moving the waste heat back out so that spot doesn't get too hot. But that doesn't change the overall equilibrium temperature.
So you can have datacenters in space, you are just not allowed to use them
Not using them would also solve all issues with cosmic radiation.
But are they doing work internally that generates heat? Genuine question.