Err, sounds like it's overheating. My fat classic PS3 has this same problem, you can "cure it" by elevating the PS4 off the surface it's on by like 1 inch with a couple of thick books or wooden blocks, and you may need to point a fan at it to blow air there so the heat from the bottom can dissipate, you MAY even have to resort to pointing an air conditioner at it to get cool enough air.
If it was fried, it wouldn't start at all. If it's still under warranty contact sony and see if they'll replace it.