A^2,
Take a flat piece of sheet metal. Heat a spot to orange with an O/A torch. Let it cool. It won't be flat anymore.
That's a lot different than a turbine shaft cooling unevenly; I'd be surprised also if one of those took a permanent set. A back of the envelope calculation might very well show that the maximum stress in that situation is a small percentage of the yield strength. But absent that, I'd probably hesitate to say a permanent set was impossible.