Before you start getting too worried about your AR-15 rifle overheating, know that AR-15s are expected to heat up through regular use.

As long as the barrel isn't turning red and drooping down like in a cartoon, your rifle is probably fine (as long as the issue is not that you're abusing your rifle).The original M16s were designed as select fire infantry weapons for short full automatic firing and not to replace heavier machine guns.
 

How Many Shots can the AR-15 Rifle Handle?

It's to be expected that after around thirty rounds, your barrel is going to become quite hot, but as long as you have a quality build, you can safely fire hundreds of rounds in a day without doing any damage to the barrel.

If you started out with bolt-action rifles, what you were probably told is that you want to stop shooting once the barrel becomes too hot, as that's going to lead to some permanent damage. This