Is your 360 bought recently?
Is it one of the White 360s? You probably got one of the older models so maybe the cpu in the 360 might be overheating quicker than it should, which leads me to believe that a) you might not have it well ventialted, b) it is really the cpu's fault and I would then suggest you trade it in for a good newer 360 model where that problem was fixed.
I've been playing CoD4, Orange Box(more of this one recently), Ace Combat 6, and Assassin's Creed the heck out of on my Elite, so far no problems.