Wouldn't the operation of an AR or AK type of rifle be hotter in general
No.
All types of gas operated firearms use expanding hot powder gas to operate the action.
That generally occurs 10" - 14" up the barrel on a rifle, where the gas port is drilled into the bore.
In an AK, or AR, none of the hot gas from the gas port in the barrel reaches the fired case.
In an AK, the gas piston cycles and the hot gas is expelled well in front of the chamber.
With an AR, the gas is directed back through the gas tube, into the bolt carrier, where it drives the bolt carrier backward off the bolt to unlock it and allow case extraction and ejection.
Yes, a DI AR-15 runs hotter then a GP AK-47.
But neither one has anything to do with transferring heat to the fired case.
By the time the hot gas gets to the gas port in the barrel to do anything, the bullet is gone, the fire inside the chamber is out, and the pressure has already dropped enough to allow case extraction.
As a matter of fact, the fired case carrying off heat from a full-auto firearm is a design criteria.
If the brass didn't carry excess heat out of the gun fast as it was fired?
The gun would eventually melt.
Food for thought:
An AR-15 can cycle at 750 to 1,000+ rounds per minute in full auto operation.
For the math challenged like me?
Thats 12.5 to 17+ rounds per second getting fired and ejected,
per second.
How much heat transfer from the case to the chamber to cool the cases do you think can happen in that length of time??
Or, lets see you run a bolt action that fast and eject hot cases!
rc