If you're shooting it off a bench, with bags fore and aft, then yes the heavy barrel will retain accuracy better as the barrel heats up.
If you're not shooting off a dead rest, then there isn't a difference. If you're using the mag as a monopod, you can't shoot the difference. If you're shooting off a sling, you can't shoot the difference. If you're resting the fore-end across a pickup bed rail, fence post, or anything else, you can't shoot the difference.
Using the light barrel, I can shoot high into the expert rating, and that's sustained fire included.
In other words: If you use your carbine from a dead rest, like some kind of extremely inefficient benchrester, then you want the heavy barrel. If you're using your carbine like a Rifleman would, then there's no need for the excess weight.