Radiative vs. Convective Cooling
> ... but surely something can be done by putting computing power outside the life supported areas.
One must keep in mind that up there in Low Earth Orbit, there is almost no atmosphere (i.e., zero, for practical purposes) outside of the spacecraft to allow for the efficient transfer of equipment-generated heat into a surrounding medium, which would then be carried away by kinetic and/or convective processes.
The only real way to get rid of the heat is by dissipating the energy into the surrounding near-vacuum "photonically" through a phenomenon known as "black body radiation:"
Since direct thermal radiation into a surrounding "empty" void is a very inefficient process (compared to the kinetic/convective transfer of heat between two materials in close contact, like a PC's CPU heat sink with the surrounding atmosphere), heat generated by the station's equipment would build up very quickly if there wasn't a way to get rid if it in a timely manner.
The station maintains its temperature balance by using closed-loop water systems to carry excess heat to giant external radiating panels, which dissipates the heat as thermal (infrared) radiation.
Another way to use this excess heat would be to pass it across a thermocouple, so the excess heat could be converted into electricity for use in charging batteries and running low-power experiments. I wouldn't be at all surprised of the station already makes use of some of its excess heat for this purpose.