I've shot lot of light bullets through a lot of barrels, and in my experience it takes a HOT barrel and a very thin-skinned bullet ay very high velocity to cause problems.
Some years ago was shooting prairie dogs in Kansas in 100+ degree weather, with ammo using a new thin-jacketed hollow-point bullet from a major manufacturer. I was shooting a .223 and my buddy was shooting a .22-250, and he got the barrel hot enough to burn the forend of his walnut-stocked rifle. There weren't any flames but there was smoke, and we had to dip the rifle into the melted ice-water in a big cooler to put it out.
The other thing that happened was that even after cooling down his rifle in the water, after a few shots accuracy went to hell. We finally shot it on paper, and not only were the shots from a hot barrel scattered, but you could see a swirl of lead around each bullet hole. This didn't happen with the .223, no matter how hot it got. Both rifles had the then-standard twists for each rifle, 1-12 in .223 and 1-14 in .22-250.
Was also once shooting a VERY fast 6mm wildcat on PD's which belonged to a friend of mine. It had a 1-10 twist and after the barrel got warm some bullets didn't make it far. There'd be a puff of something dark maybe 5-10 feet in front of the muzzle, and no bullet strike downrange.
But I've yet to see anything like that happen with a .223 of any twist. Not that it couldn't, but it would take a heck of a lot of heat, probably enough to start cooking off rounds.
