This is good information, except-
Barrel heat is indeed a factor for any barrel that has not been stress relieved. The button rifling process introduces stress into the steel that can and does cause shifts in the point of impact as the barrel heats up. If this were not the case, high end barrel manufacturers would not spend the extra money to have them heat treated (stress relieved).
Also, the thinner the taper, the more quickly the barrel heats up and the more it's groups can open up.
Benchrest shooters do indeed fire strings very rapidly when a favorable condition exists. They fire them through high quality, bull contour, stress relieved barrels, using rounds that burn a relatively small amount of powder, such as the PPC's or BR's; thus barrel heat is not an issue for them. It may, or may not, be for the OP. I was simply suggesting that he might want to test this out, because i have dealt with similar problems with factory barrels myself. I have two that will not group well for five shots fired consecutively, but do much better if given time to cool thoroughly between shots. These are hunting rifles, not benchrest rifles.
A high quality properly stress relieved barrel can be shot until it is very hot without much loss of accuracy. Most factory non-stress relieved barrels will not behave as well when hot.