Of course this doesn't solve the myriad problems, but it does put dissipation squarely in the category of "we've solved similar problems". I agree there's still no good reason to actually do this unless there's a use for all that compute out there in orbit, but that too is happening with immense growth and demand expected for increased pharmaceutical research and various manufacturing capabilities that require low/no gravity.
Imagine a liquid which can be electrically charged, and has a low boiling point.
(Ask 3M/DuPont/BASF/Bayer... - context 'immersion cooling')
Attach heat-pipes with that stuff to the chips as is common now, or go the direct route via substrate-embedded microfluidics, as is thought of at the moment.
Radiate the shit out of it by spraying it into the vacuum, dispersing into the finest mist with highest possible surface, funnel the frozen mist back in after some distance, by electrostatic and/or electromagnetic means. Repeat. Flow as you go.