I think you got the cooling problems backwards. In vacuum it's a lot harder to get rid of excess heat than it is inside an atmosphere. Latency might be a bit of a bummer.
The Outer Space Treaty specifically says that no country can claim sovereignty over outer space or celestial objects, that countries retain ownership of anything they launch into space, and that they are liable for damage they cause to any other countries space objects (or people on them). The treaty has been signed and ratified by all major space faring nations, including the US, Russia, China, and all major European countries.
Might this be an idea for the future of DNS and highly-independent web hosting in some form? No cooling problems for shure!
Of course, there's the minor issue of a connection to the wired internet...
I want a .orbital TLD!
Forget the "cloud" how about "space"?
Hmmmm, isn't there a prominent web entrepreneur who's building a rocket company?