How about an array of orbiting servers?
Servers need energy and cooling, and outer space has quite a bit of clean solar power and of course low enough temperatures to keep equipment cool for a long time. Does that give you any ideas? It certainly inspired the folks at server-sky , who are working on the specs for an array of orbiting servers, transferring computation to where it's potentially cheap and using it to serve the needs of the underserved on earth.
Server Sky thinsats are ultralight aluminum foil substrates that convert sunlight into computation and communications. Powered by solar cells, propelled and steered by light pressure, networked and located by microwaves, and cooled by radiation into deep pace. Arrays of tens of thousands of thinsats act as highly redundant computation and database servers, as well as phased array antennas to reach thousands of transceivers on the ground.Of course when they gain sentience and turn against us by blocking out the sun, then we'll be sorry.
First generation Version 5 thinsats are 20 centimeters across (about 8 inches) and 0.04 millimeters (40 microns) thick, and weigh 3 grams. They can be mass produced with off-the-shelf semiconductor and display technologies. Thousands of radio chips provide intra-array, inter-array, and ground communication, as well as precise location information. Thinsats are launched stacked by the thousands in solid cylinders, shrouded and vibration isolated inside a traditional satellite bus."
If your server room's at 60 C, you need to invest in better air conditioning.
Quite seriously, convective cooling is so much more efficient than radiative cooling that for any realistic setup, servers on the ground are going to be much easier to cool than those in space.