What model of Dell do you have? I used to have an Inspiron 5150 notebook that was notorious for heat problems and shutting down during 3D games. So much so that I had several 4-hour calls to Dell tech support to troubleshoot the issue. Twice it shut down and would not come back on even after cooling overnight. I eventually had to have the CPU, video card, and motherboard all replaced at one point (though at different times). The CPU and motherboard were on the same call, and the tech told me that the CPU had gotten so hot it had fused to the motherboard.
That model was famous for having one of the poorest case designs, having only one fan in the case that was inadequate for cooling the desktop-class Pentium 4 that was installed.
I would suggest searching Google for <your laptop model> heat problems. When I did this for my Inspiron, I found that this problem was very common with my particular model.