Rather than buying some designer case that costs $125 by the time you pay for shipping, go to Home Depot and buy a window air conditioner for $150. Not only will you be cooling off your apartment, but the ambient temperature inside of your case will never be lower than actual room temps, so lowering the room temps, could help to cool off your PC. A few other things you can do to help lower the temps inside of your case include cable management, clean the dust out of your case with a can of compressed air, clean or replace the case fans as well as the fan on your CPU. Messy cables and excessive dust will increase case temps.
For best airflow at cheapest price...i'd say a cheiftec dragon - although they can be a hassle to do a perfect wiremod, but there is space betweem the back panel and hardrive bays for cables.
Other than that, a CM stacker or wiremodded Lian Li.
I also agree with Pagan Wizard, an airconditioner or anything to lower your room temperature will do.
I went out on a limb a while back and got the tt armor case....couldn't be happier....it come with 2x120mm fans and 2x90mm fans....the entire front of the case is mesh with a 120 to help with intake and the rest are exhaust. My ambient case temp is basically room temp. But if your apartment is naturally hot...then no matter what case you get...unless you get some of those 5.25" drive bay a/c things from a place like frozencpu, the case won't help