Well, since you mention barrel heat I took my Ruger GSR to the range a few weekends ago and shot 99 cartridges over the course of about an hour and a half. The barrel was almost too hot to touch. So, depends on what you view as a lot of shooting.
I'm not a good enough shot to say anything about accuracy, and it was my first time shooting a rifle in years. Supposedly people have been getting somewhere around 1 moa, which is certainly good enough for the concept, hickok or whatever his name is has a good review of it and he actually shoots it.
What is perfect accuracy? Putting bullets in the same hole at a hundred meters?
From what I've seen lightweight and good accuracy do not mix for off the shelf rifles. A tight, accurate(sub moa ) rifle is probably not going to be light and likely not the kind you would want to use in the field.
If you're near the edmonton area I'm willing to let you try my Ruger GSR, but tight it is not. Tolerances seem pretty generous, which is good for the concept since it's intended as a rifle you can bring with you in the rain and dust and mud. I have noticed feeding malfunctions when inserting a mag on an open bolt, the rim of the cartridge gets caught on a little ledge below the bolt face so it's not high enough to get pushed out of the mag. Cycling the bolt, or inserting on a closed mag corrects the issue. Might be me as none of the other owners have had the problem.