Cold won't be an issue. Computers work great in the cold so long as it doesn't cause condensation which could short out the circuits. And if there is no atmosphere, that isn't an issue at all!
As other answers have stated, the real problem is heat dissipation. Your typical home computer you are familiar with uses heat sinks that dissipate heat into the air to keep everything within operational temperatures. Of course, without an atmosphere, systems like that are going to fail. In a vacuum there is nothing to absorb the heat, so you are stuck with the radiant abilities of your heat sinks, which isn't nearly as efficient.
Hopefully, though, on a spaceship where a decompression event is always a danger and with a crew that relies on the computers, the ship's designers took this into account and designed cooling systems that could work in a vacuum. That could be a closed-loop liquid cooling system (which hopefully has some place to dump the heat; again even a liquid cooling system on your average gaming PC that has one ultimately dumps the heat into the air around it), or a heat sink designed to radiate effectively enough into vacuum. It would be utter negligence on the part of the engineers not to design for this contingency. It should also be noted that the atmosphere on a space ship is a closed system anyway and would have to have a way to get rid of the heat if you are going to dump heat into it, or eventually you are going to cook your crew!
It could be, though, that the computer cooling systems don't work as efficiently as normal without atmosphere. Or maybe the breach also damaged this system in some way so it isn't as effective. The computer might have to be slowed down to a lower clock speed so as not to generate as much heat. Or maybe the crew has to turn off non-essential functions so the computer doesn't cook itself.
Update: Thinking about this a bit more, if the engineers who designed the computer did their job, loss of cabin pressure by itself should not affect the ship computer at all. This would been an easily-considered contingency. Relying on the life support system for heat regulation of the computer would have been a bad design decision anyway. It violates the principle of separation of concerns any competent engineer would have followed. Current space craft use radiator finsuse radiator fins to dissipate heat, and if your computer is now in danger of overheating, you probably lost some of those in the impact. To keep it running you could either reduce its workload so it doesn't generate as much heat (which may or may not be an option depending on how much work it needs to do to get you out of the crisis), or maybe stage a space walk into the decompressed room to rig up a new heat-dissipation system.