Rate of fire depends on the rifle. If it is a match rifle, or sniper rifle, the barrel should be kept as cool as possible, meaning that you don’t want it to get hot to the touch. Keep in mind that the barrel on a rifle is the wear item on any rifle.
Most match rifle barrels loose their match accuracy before 7000 rounds, and usually get replaced around 5000 rounds. The numbers change slightly depending on the caliber. Usually the hotter or higher velocity the round, the quicker it needs to be replaced.
For non-match rifles, barrels can last upward of 30,000 rounds or more before accuracy is unacceptable. I shoot both types of rifles, and even a machinegun or two. 1919A4 Brownings are shot until the rounds start to keyhole
I have a sub-machinegun barrel in 9mm that has 50,000 rounds and still looks quite crisp and is still accurate. That is at 750 rounds a minute with 1000+ rounds fired in one hour. Because the round is not as hot as a rifle round coupled with the fact that the open-bolt functioning keeps the case out of the chamber and lets air cool by passing down the bore, it lasts longer.
Believe it or not just opening the action of a match rifle and letting it cool in the open position will let you fire more rounds per hour without burning the barrel. Barrels are meant to be replaced and if you are a shooter that is worried about burning a barrel out, you need to find a gunsmith to replace your barrel.
As far as how fast I can shoot and still hit, 12 shots a minute is not hard to shoot under 2 inch groups consistently, and better than that with some guns.