Laptop randomly dies?

Wow I can only think of one theory I think that your laptop not being hot while playing a game is a BAD THING BAD! the thermal paste probably degraded allot over time. Your hardware is probably overheating soo much to a point where it's shutting down to prevent damage , Clean it with an air duster and replace the thermal compound on the CPU and what not , if you don't know how to do it take it to a professional IF this is the case. Otherwise I wouldn't know lol