The Leafeon Pinkeh

Sounds a lot like the overheating safety system activating. It turns off your computer if there's a danger of some of your hardware getting melted from overheating. Pump some dust out of your laptop and try again. Do you use it on your bed?

He said it's not overheating, but the dust issue is worth considering as well.

Too much dust can stop the fan from rotating fast enough, which the computer recognises as an overheating hazard. If you don't have a pump handy, just blow the stuff out.