I am trying to play call of duty 2 on my computer and it plays perfectly for the first 5 mins then starts lag.?

I am trying to play call of duty 2 on my computer and it plays perfectly for the first 5 mins then decides to lag. Ive tried playing in compatibility mode and that helped for a little bit but then the lagging started again. My computer should not be having these issues it has 4 gigs of ram, 500 gigs of mem (more then half is still free), windows 7, and a nvidia video card. I was expecting this game to work perfectly on this computer and its a real disappointment that its not. Any help would be greatly appreciated. I just wanna get it running smoothly.