>I wonder if the cooling required for nuclear reactors could involve the void?<
Yes, you would use radiators on the shadow side of the spacecraft to radiate the heat into space. Heat management in the vacuum of space is actually quite a tricky thing. With no air or other fluid to take the heat away (like with a CPU heatsink) you have to use radiation and the more heat you generate the larger the radiator has to be. Consequently radiators for a nuclear reactor similar in output to that in a nuclear submarine will have to have a large area, in the order of several hundred to a few thousand square metres, of radiating surface.
This will only be needed for the power generating reactor though, the nuclear rocket engines would be cooled by the propellant (typically hydrogen) being fed into them picking up the reactor heat. The heated (and expanded) propellant would then go blasting out the nozzle of the engine producing thrust and carrying the heat away too.
Hope this is of use/interest