IDEA #3:
You can also try making a cheap 5-gallon bucket Air conditioner. Check out this video here: https://www.youtube.com/watch?v=HxSLbpAwibg *Someone commented on why this would not be good.
IDEA #2: Now that you added the fact there's no window in the room I have another idea. How about you move the computer outside of the room and just run a longer cable under the door to connect your monitor. That way, the computer won't make the room hotter. You can also use wireless keyboard/mouse or get cheap USB extension cables. All the cables you would need can be purchased for cheap online.
OLD IDEA #1: You can do something like this image below. Basically, you get some ducting from a hardware store (shouldn't cost too much) and then re-route your computer's exhaust fan to go straight out the window instead of blowing the hot air into the small room.
