Its not overheating, laptops normally shutdown completely and cut off power supply if core temperature is too high.
Put it through a stress test, that would probably be the most accurate way to see whats going on. Watch videos, mass download, try playing some high req games like FPS (if u got graphic card for those), and see what tingles it the most. Also disable teh wireless adapter and see if it crashes after that. And try instead connecting with cable to internet (if your wireless adapter/router is somewhere close by).

And whats up with 32-bit Windows 7? Shouldn't that kinda stuff be eradicated? I'm not really following the latest trends.