I don't know if the heat can affect fps but it'll eventually affect your gpu if the heat is too high. You should check what temperature you're getting when playing games (or is it only this game?) if it goes to somewhere like 100 celsius then it's time to do something.
I used to have an 8800GT and that sucker whould whislte line a sob when I played games. I think its the dust that collects on the fan on the card.
It could be that. Could be a failing fan as well. Personally, I have 6 case fans blowing air into/out of my case. One is a SUNON KD1208PTB2 (From the old internet vendor OneCoolPC) that moves as much air as a desk mounted personal fan. It is also so loud (and has a high pitched sound) I can hear it upstairs at the other side of the house.
However, after running JC2 for 10 hours straight, my CPU heatsink is cold to the touch and there is no heat buildup in the case what so ever. My power supply fan NEVER comes on.
If there's a tiny fan *under* your video card, on the motherboard, it's probably a northbridge heatsink fan. These are usually smaller than CPU or GPU fans, so they spin faster and can make loud, high-pitched noises when dusty or worn out. As the game shunts huge amounts of data to the GPU the northbridge will heat up, and as the GPU renders it will heat up as well, so the fan will likely kick in once you start playing the game. The heat won't directly affect your frame rate but if the computer gets too hot the CPU, GPU, or northbridge can start having errors.