Yes, CF acts like an insulator compared to steel. It does trap heat in the barrel as it doesn't allow it to dissipate into the atmosphere as efficiently as steel does. Styrofoam has around 0.03W/mK thermal coefficient. I'd call styrofoam an insulator.
A CF barrel has less Thermal Mass than an all steel barrel and this causes it to have less Specific Heat Capacity than the steel barrel. As a result of that and the fact the heat cannot escape as quickly, the temperature of the CF bore core will rise higher and faster than the bore of an all steel barrel given the same loading and tempo of fire.
Some people on this website have suggested having a fan blow on the barrel to help cool it. I think it would be more effective to blow cooling air through the bore. Water would be a much more efficient bore coolant but I'd be very hesitant to use it as it could cause thermal shock to the barrel and damage it. Depending on how hot the barrel is you might even get scalded by the steam.