Well if you wanted to go all-out-robotics-style on this, you could try building a thermocouple peltier effect cooling array
out of these. The first few on the page are the same as ones used in those nifty take-with-you-in-your-car thermocouple based cooler/warmers. Just remember that these MOVE heat, they don't just get cold, so you'll need a cooling fan and a place to blow the heat (probably just hang a hose out your window if you have to, or put it into your attic, something like that.
Building an enclosure for this out of plywood and insulating the inside to keep the heat from reentering the room, then using some surplus kit fans from the FRC kit should work for moving the hot air out of the box down your hose. A large PC power supply should do the trick for supplying 12VDC to your thermocouple array(s). Wow now i wish this was my project!
-q
p.s. each one of the first junctions shown on the page is equivalent to about a 275btu/h air conditioner, so 22 of these babies gets you up a little past a 6000 BTU/h energy transfer rate, about the average for mid size window air conditioners. its a little pricey... but man is that cool! (no pun intended
)