There is a very good chance that it is overheating either the CPU or the graphics--but this sounds like CPU overheat. So forcing a bit more air through it might do the trick. Sometimes the little fan will fail.

There is one other thing I've seen happen with laptops: sometimes the transformer lacks the capacity to run the machine at full load for more than a few minutes. I had a not-so-bright boss illustrate this for me when he used a smaller transformer from an older machine, because it fit in his luggage better. His machine would shut down after about 15 minutes while we were running simulations. Our laptops were very similar, but I noticed he had a smaller, lower capacity transformer. When I asked him about it he said, "Yeah, it came with one like yours, but this one is lighter and fits in my luggage better." He used the bigger one after that, and the machine ran fine.

Some laptops run "throttled" when on battery power--the P4's I had ran at much lower speeds on battery to conserve power...of course, that didn't help with simulations that needed to do X calculations...it took longer, and during that time was powering the display as well.