Considering it has a top mounted PSU, and the 7750 shouldn't produce too much heat, I think you'll be fine. I had a similar concern when I put a HD6670 in an HP case a year or so back. I had also upgraded the PSU then so I essentially had a 135MM Exhaust fan at the top of the case, and 80MM fan to help expel more heat as well. The case had small grills all around which provided some fresh air (Negative air pressure inside the case I think, since all were exhaust, air would naturally come inside the case).
If you do run into some issues later on, however (which I highly doubt), it's as easy as leaving the side panel off so the components can get fresh air