I can not believe I am going to waste my time getting involved in this but there are three forms of heat transfer. Radiant heat matters. Thermal diffusivity matters. Naysayers can say what they want it just proves they know nothing of heat transfer. I am not going to claim one barrel cools or heats up faster than another because I don't know their specific proprietary properties of the different carbon/resin make ups but if you are hung on specific heat capacity/thermal conductivity it just shows you don't understand heat transfer.
In any case who cares how fast your barrel cools? The number one reason to buy a carbon barrel is to have a stiffer barrel for the weight and ultimately a lighter rifle. They are also capable of the same accuracy as a steel barrel. I will not post in this thread again. If you really care to hear about real world experiences PM me. Have a great day.
My newest Christensen barrel chambered in 300WSM