Custom Built Computer CPU dead?

I built a new computer for my friend and after booting for 5-4 mins it would shutdown i couldnt even install windows, i then checked the pc health and the cpu was at 85c and just booted for 1 min i know thats a high and have stopped and am buying a new cooler for it since the one current is the stock, we've tried booting about 10 times before and have stopped since knowing it is really hot, do you guys think the cpu or any of the parts might be damaged during all this overheating? i heard the comp auto shuts down if it reaches temps too high. is the cpu dead? we'll find out till we get new cooler to replace the stock but can u guys give me predictions on what is going to happen?