Do they need to? I wonder how feasible it would be to put large computational centers in space and have space solar farms powering these computational centers. So if we want to test complex or long-running programs/models/algos, we can just beam it to the computational centers orbiting earth and wait for the results when it's finished.
Radiators. Need pretty big ones if the computers want to run cool.
Probably would be better to manufacture most of the stuff on some asteroid or on Mercury and have the computation radiation shielded by a significant mass.