I agree with IShadowWolf on this one. Although a lot of people are having there computers turn off on them, your
After a few minutes only will the computer come back to normal
is precisely how a computer reacts when it over heats. And SC2 has a history of overheating some systems/dirty systems.
If it's a desktop, open it up and use a compressed air can to blow every visible bit of dust out of the case, including off the components. Be sure to get under the CPU fan and blow out the heat sinks. If your GPU has a fan do the same (get under it). If you are comfortable removing components, it's easiest to take them out and get all the dust you can of them, then replace them. If you're not comfortable, just leave them in. Then with it all cleaned out, turn it on and make sure all the internal fans start up. All of them. CPU, chassis(es), GPU if there is one, etc. If you have sponge mesh between your chassis fans and the chassis, clean those off as well; they're like a dirty air filter on a car if they are plugged with dust.
Like ishadowwolf said a small stand up fan works great especially if your desktop is in a desk cubby (bad circulation in those sometimes).