The resin and particularly the carbon fiber does NOT transfer heat very well (typically, that's one of the positive attributes that it's often used for in other applications) . . . any way anyone, including Proof, wants to slice it. The barrel isn't hot to the touch because of the insulating the carbon fiber wrapping provides. Tests have shown that steel transfers heat faster than any carbon fiber material.
What makes a carbon fiber barrel attractive is that it's really tougher and stiffer than an all steel barrel, AND it is lighter. This makes it great for packing around for hunting. Oh yes . . . a carbon fiber barrel does look pretty cool, IMHO.