Too hot to touch? That must be thousands. My AK gets toasty after 30 and unpleasant after 90 and scalding after 120, all fairly rapid.
My 15-22 has fired close to a thousand in groups of 150 as fast as we can load the mags and barely rated warm. I don't often do mag dumps with it but I have once or twice.
I've put several hundred rounds through mine in a session. The barrel has never gotten too hot to touch. In fact, it just barely gets warm. This is a 22LR, not an AR or other high velocity rifle.