Not a physician, but wouldn't space be terrible for heat dissipation?

Also not a rocket surgeon, but to my understanding, modern satellites already have solar panels and radiators that account for the system's overall energy absorption and dissipation in low Earth orbit [1]. Therefore, plugging a supercomputer into the solar array instead of another instrument would likely not affect the overall heat profile meaningfully. Most energy in LEO is ultimately derived from solar irradiance and passes through the spacecraft regardless of internal usage. That said, take this with a grain of salt due to the aforementioned lack of astrochirurgical bona fides.

Edit: Added some primary sources [2][3][4], including an interactive website by Andrew McCalip which lets you play around with the unit economics of orbital 'datacenters' at various price points [4].

[1] https://youtu.be/DCto6UkBJoI

[2] https://services.google.com/fh/files/misc/suncatcher_paper.p...

[3] https://starcloudinc.github.io/wp.pdf

[4] https://andrewmccalip.com/space-datacenters

Yes, you would need massive amounts of radiators