Bart, you got me wondering enough that I did some research. Here is what I learned and how it affects the barrel.
Steel expands with heat at a constant that is calculated with a coefficient and the difference between starting temperature and final temperature. The same formula is used for all thickness and diameter pipes. A barrel is essentially a pipe. That shows that the barrel will expand in length the same amount regardless of thickness.
Therefore if the barrel is squared to the axis of the bore then the barrel will not move off of it axis due to thermal expansion.
You can't fix stupid....however ignorance can be cured through education!