With radiators just like with every existing satellite system.
https://youtu.be/DCto6UkBJoI&t=12m57s
Very large scale datacenters would likely have some nasty fluid handling problems to solve.
I'll just note that I am not a fan of putting internet infrastructure in space. I think polluting the upper atmosphere with a bunch of metals every time a satellite deorbits will certainly have negative consequences. So IMO space should be limited to things we can't do with earthbound infrastructure.