Full auto MG's can't take continuous fire, they've been water cooled, or needed to be cycled in bursts to keep the heat load from exceeding the working temperature of the barrel.
That alone should put to rest the myth of the case carrying off heat - but no, it keeps popping up. Well, add open bolt actions, which are used to allow air into the chamber and barrel to cool it. Submachine guns fire from an open bolt, and Colt even has a combo action that fires closed bolt for accuracy, but when it warms up, switches to open bolt without the operators intervention. I haven't seen or trained on a MG in my career that didn't. MG's don't load rounds into hot chambers to cook off, they stop in the open bolt condition. Moot point what a cartridge will do - it's accepted it WILL cook off.
All that was invented and made reality with brass cases supposedly carrying off all that heat - which they simply can't do all that much. If the M4 video of full auto firing until the barrel explodes doesn't tell you that, or stories of soldiers pouring water on MG barrels in combat, then the physics in numbers won't either.
As for "caseless," the LSAT polymer cased round can fire full 100 round belts, there's plenty of video released by .Gov to show it, and tests are scheduled for Battalion level exercises. That's 400 weapons being used - not just a lab sample knocked up out of one off parts.
Look at the evidence right out there and come to your own conclusions.