I've got a Savage Model 10 in .243 that strings vertically as the barrel heats. It's a very accurate rifle when I take my time, but if I start pouring them downrange, the barrel will get hot and the shots will start walking up the paper. The rifle is free-floated and pillar bedded, but not glass bedded. As it's a hunting rifle and not uncommon for me to only shoot three rounds through it for a whole hunting season, I don't worry about it much. I've got it sighted for the cold bore shot. The critters don't seem to know that it will string vertically.
One interesting thing, though. One summer I wanted to see if different ammo would help it act right, and I bought some factory ammo, and handloaded a bunch of different loads and bullets from 75 to 105 grain. Probably a total of 20 different loads. Later I made a composite target and it shot everything, EVERYTHING into a three-inch group at 100 yards.