Comment by trynumber9

AMD's first Athlon chips did not run particularily hot. They needed a fan, just like Williamette chips, but actually used less power than the competition. The difference was they had no internal, on-chip diode. If the heatsink and fan fell off, then the chip could cook itself. The boards had a thermal sensor to initiate shutdown if the fan stopped working. But it's debateable if it would detect it quickly enough if the entire cooler fell off.

In that scenario, shutting it off seems better. But it might roast itself on start up anyway.