Being a retired metallurgist and very familiar with the manufacture of long transmission shafts I'll chime in.
Any steel harder then HRC 30 will have stresses put in from machining, straightening or forming. What is typically done is extra stock is left for finishing operations and the shaft, barrel or whatever is "stress relieved" after these operations which causes them to warp. Then they are finished using processes that do not put any stresses in them. If they are not stress relieved that stress relieving will take place when any higher heat is applied.
The shafts are heated to 1650º F (typically) and quenched.
They are tempered to the desired hardness (1100º F for HRC 30-32).
They are machined, straightened, drilled, hammered or whatever and then receive the stress relieve at a lower temperature (1000º F) then the tempering temperature so as not to lower the hardness.
Then the finishing operations are done.
It takes alot of heat to cause these non-stress relieved barrels to warp (300º F or more) which is much higher then firing the rifle will yield SO the most likely cause of barrel warping is a bore which is not concentric to the O.D of the shaft or barrel. The different thicknesses will cause a change but since this temperature is low I would expect the barrel to go back to it's original shape. If you only fire shots out of a cold barrel you would not notice it walking.
My 2 cents.