Do you have temperature readings in the drivers??? I dunno about gigabyte 6600 cards, but there is a sensor in the GPU for temp, and some manufacturers actually let you monitor it. I have temperature readings from my 6600GT, it should be in the drivers under temperature settings. If not, you may want to consider hacking your bios to enable this feature, it might be worth while for troubleshooting. If you do have it, you should have idle temps around 40c, 50c tops. Load should be under 80c, if your temps are higher than this, you have a problem with the contact between the GPU and heatsink, or airflow in your case. The heatsink will get warm, it's supposed to! If it didn't get warm, I'd be worried. What happens when you run with the side of the case off??? Maybe point a household fan into the case to help it out, just to see if it is heat. Two fans IS NOT ENOUGH, I have a 120mm on the back of my case, another in the PSU, and 2x 80mm fans for intake in the front! That's enough to cool a system. I'm betting the problem is heat like you suspect, or it would have issues all the time. They make card slot coolers that go into the PCI slot covers on the back of the case. One pointed @ your video card might do wonders if that's the case.
Usually puking with a new graphics card is a sign of a weak PSU (powersupply), how are your voltages??? As for AGP voltage, it does nothing except heat up the HSI chip on those cards. It's a pointless adjustment, you should leave it 1.5v. The GPU draws off the 12v rail, so see how that looks, if it's going under by 3% or more, time to worry. What kind of PSU do you have, if it's cheapie, that might be part of the problem! It is probably heat though, but check it out anyways.