Space isn't cold... it's empty.
I'm building on a number of answers here and would like to point out that the answer you selected as the "best answer"... isn't... (all due respect to @ChristopherJamesHuff, who kinda answered the question but didn't adequately explain anything).
Your problem isn't heat. Your problem is the transfer of heat away from what's generating it. If you don't do that fast enough, the object generating heat (your computer) burns up.
On Earth we have gases (usually the atmosphere) and liquids (you should be thinking "radiator fluid") to do that for us. But even that's often complicated. Let's consider your car!
Your engine (OK, the engine in my car...) is burning a not-quite-as-aptly-named-as-we-once-thought fossil fuel. Nothing's perfect, and as a result the tiny explosion that moves a piston also generates heat. We don't want the heat. In an ideal world there wouldn't be any heat. A massive amount of electronic engineering is dedicated to minimizing the generation of heat! But there's heat. What's next?
Your engine block has tunnels in it that allow the passage of a fluid — radiator fluid, to be specific. This fluid and the tunnels in the engine block are specifically designed to transfer as much heat to the fluid as is humanly possible as quickly as humanly possible. But this isn't enough! There's a finite amount of radiator fluid and although it's great at sucking the heat out of the engine block, it can only absorb so much before it first boils, then vaporizes, causing all kinds of trouble.
So the next thing that happens is that fluid runs through a radiator that allows the heat to move from the fluid to the atmosphere. It's technically true that the atmosphere is finite... but compared to radiator fluid, it's infinite and can absorb an infinite amount of heat.1
To make my point, we moved the heat from the source (combustion) into the engine block, then into radiator fluid, then into the atmosphere.
The problem with space is that it's empty
No atmosphere. Certainly no fluids. There's nowhere for the heat to go.
A computer on the ground that needs a couple of cubic inches of heat sink to vent the heat to Earth's atmosphere needs cubic feet of heat sink to vent the heat to the precious few atoms that can absorb it in space. That's the problem. There's pretty much nowhere for the heat to go.
Why, then, do we think space is cold? Because where there is nothing to hold heat, the result is the perception of cold. Why the perception of cold?
This is really important!
The nature of the universe (all of the universe) is to move to the lowest energy state. We call this "entropy." Things don't want to be hot. Energy wants to even out and stabilize. When you take away the source of the heat, the result (over time) is that everything falls to a minimum temperature. We call that "cold" because we're conditioned to living under the beauty of a blazing sun.
But the truth is, space isn't so much cold as it is empty. In the middle of all that empty the energy, through entropy, has minimized and the result is "cold." But that doesn't mean you can sink heat into it. After all, if the blazing glory of the sun can't heat up space, why should your itsy-bitsy computer?
It would be better to put your computer on Antarctica where there's both a lot of cold and a lot of gasses and fluids to draw away the heat. But if you insist on space, you'll need massive heat sinks to transfer the heat to what little mass there is out there.
Heat must be transferred through something. In a perfect vacuum (which space isn't, thankfully!) there isn't anything heat can transfer through.
1 This isn't actually true. While a minor component of climate change compared to polluting the atmosphere with greenhouse gasses, the heat generated through combustion is nevertheless part of the problem. The atmosphere can only hold so much heat, too, without consequences. Like melting ice caps.