Watch your television in the living room, like a civilised human being, then.
:p
But yes. Watching streaming video shouldn't impose the kind of load that causes a modern CPU to thermally cut-out. Unless you cook it, like it sounds you did.
As you have discovered, in addition to making you an uncivilised colonial baboon, using a laptop in bed is double trouble - not only is it trivial to block the vents, but also you don't feel the warmth if your duvet is thick.
Try stress-testing it in ideal conditions (on a table, frample), and see if it repeats.