Gobc is absolutely right.
Thermal conductivity (ability to transfer heat) in W/m•K:
- Steel is ~ 50 (carbon) to ~8 (high stainless)
- Carbon Fiber in Epoxy 5-7 in plane 0.5-0.8 transverse
- Air (not moving) 0.026
This is how "plane" looks like:
This is how transverse looks like:
Notice at direction of the fibers withed along the barrel or melted standing up.
Anyway, you see that steel, especially carbon steel is conducting heat way better than any fiber. But more importantly AIR is conducting heat WAY WAY less.
Regardless, the heat is created in the inner barrel and it is transferred in steel to outer barrel. You can't possibly "pull" more heat from the inner barrel "faster" then steel between inner and outer barrel can transfer. Think about regular cooler with food. No matter how your wrap it outside with foil, copper, put it in water or whatever - the inner temperature will be stable because it is locked by the amount of heat transferring thought the thick plastic sides of the cooler.
Your problem is also not the conductivity of outer layer barrel itself, but the heat conductivity of surrounding air and air thermal capacity (how much heat it can suck into itself without transferring it further).
The only way to significantly increase heat transfer from a barrel is either add a significant heat absorption - think water jacket for instance like maxim mg. This is because water has excellent thermal capacity and can "suck" heat into itself and you can put move water from and our of the jacket. Or, second option, significantly increase square of the outer surface contacting with air, adding fins or increasing barrel diameter.
Anyway long story short, carbon fiber wrapped barrel like this:
is in fact more insulated from the outside and will heat up INTERNALLY faster and cooldown internally slower then simple steel. If the whole idea of cooling down or transferring heat from a barrel by applying any material outside of a barrel could possibly work, we would see copper (401 W/m•K) or aluminum (205 W/m•K) sleeves or barrel jackets long time ago. There was plenty of copper and aluminum in the last 150 years to work with, but no one put it outside machine gun barrels so they would heat up less cool down faster.
It is pure marketing BS. For extra money I'd rather have my barrels gold plated (310 W/m•K by the way)
