Is there a way to test the video card in another PC ?
The AMD cpu you are using (X2 4450e) is really low power (50 watts or less) and so is your video card (under 60watts). I really can't see how you would be using more 12v then your current PSU can supply. Even assuming a huge 35 watts for the MB, chipset, etc. that's only 145 watts or about 12 amps of 12v.
Is the sticker on your PSU visible? If so what is the amp rating on the 12v rail? I'd guess it's much more than 12 amps.
Maybe send XFX a note and see about an exchange?
Were you able to try logging the video card temp with GPU-z (or equivalent) ? Lower temps are always better but noise is not your friend. The case was designed to handle the type of heat load you are generating. Agree with Bucknutty that blowing air out the back is the right direction. I'd check your MB and see if it has a header for a temp controlled fan. If not I'd get a low speed fan or a fan with an external speed control. Having a hurricane blowing thru case while gaming is OK, while playing movie or listening to audio or browsing web silence is golden.
fyi: saw this comment at newegg "Other Thoughts: I slapped in a Radeon HD 4670 and can run WoW and Wolfenstein: ET at full settings. Uppgraded the PSU to a Thermaltake Black Widow 450w."
http://www.newegg.com/Product/Product.aspx?Item=N82E16883109029 implies you can get normal size atx psu in case. Do you have another 1.5 inch of clearance ?