Hi,
I had the same problem, my laptop is less than a year old. It would shut down after long periods of simple surfing, however whenever i tried to play a game it would shut down after about 5-10 mins.

I tried opening up the laptop, Satellite A300D but it was a little more intimidating then i thought it would be so i settled with blowing pressured air through the fan outlet and all the other openings and that seems to have done it for me. Now can feel alot more air coming out and its still cool after 30mins.

worth a try before opening it up, but thanks for the info.