Sounds to me like a barrel with some inherent stress in the steel, for whatever reason.
I've had some barrels like that, mostly factory but some custom. One really lightweight .243 Winchester barrel shot like crazy when hot, as in 5 shots under 1/2" at 100 yards, but the first three shots never averaged much better than 1-1/2", no matter what modifications were done to the rest of the rifle.
