-
Hunting rifles, especially lightweight ones, are not designed to be constantly putting lead down the tube. When I go to the range for practice, I'll bring a couple of rifles so I can shoot a few and then let the barrel cool. I use a .223 for squirrels and I'll shoot five rounds, then let the barrel cool while I use a .22lr, then pick up the .223 again. I still get to shoot plenty of varmints this way.
Not knowing exactly how you arrived at the overheating problem, I'll speculate that it may have more to do with your expectations about how many rounds you can shoot before having to give the rifle a rest and less with the quality of the rifle. I've been very happy with both the .223 and .243 I own (both T3 Lites).
I let my .30-06 have a rest after putting a few rounds through it as well, and I do most of my shooting before 10 AM.
