Technically, an overly open case is not very well cooled. You need airflow, not dissipation. Depending on how many fans you have, and their position, it might be a good idea to block off useless vent holes. Nevermind, saw the picture. You don't have a lot of airflow on that at all, from what I can see. AFAIK, a card will generally run as fast as it can if you don't have something limiting it. There's software out there to stresstest a card, and look at temperatures. IIRC, rivatuner does it for Nvidia. It may have a temp monitor built into the nvidia software: ATI's CCC has overclocking, temperature, fan control.
If you add any fans, make sure they point the right way. try and keep them relatively balanced between intake and exhaust. In the worst case, if you're willing to put up with cleaning more, a tablefan can keep it cool if you open the side, until you get a new case or different fans.
fakedit: He has a top mounted PSU, which won't interfere with card. Having one with a moderate headroom over intended output will make it cooler as it doesn't have to run close to its peak. You might want to list off where the fans are on it, as there's only one picture there.
realedit: oooh nice, you got one with an i3 instead of the Athlon II.
As an example of airflow, I'm using a Coolermaster Centurion 590, which has a 120mm fan on the front, two on the side over the card and processor, 1 on the top back, and 2 on the top, with the PSU on the bottom and isolated. The air is drawn in from the side and front, passed over the hot crap, and ejected out the top and rear. Hot air rises, so generally top-mounted fans are damn nice for exhaust.