Carbon fiber dissipates heat amazingly fast. I used to heat up my HMR barrels fairly fast until I put a VQ barrel on, it takes a LOT to get it warm.
Actually this is a misnomer. Your steel barrels got hot fast because they absorbed the heat from shooting much faster as metal is a better conductor of heat. Materials that conduct heat very well also give it up very well. Pick up a hot wood block and a hot steel block at identical temperatures. Which one feels hotter initially? The steel block, because it absorbs, and subsequently dissipates heat much faster than wood, which is a poor thermal conductor.
A material with poorer heat conduction will absorb heat at a slower rate, giving the illusion that it is somehow dissipating better than steel because it isn't as hot. To take things to an extreme, wrap your barrel in asbestos and it'll take forever to heat up. Does that mean asbestos dissipates heat amazingly fast? No, it's just poor at absorbing heat, and its poor at giving it up. If your heat sink doesn't feel warm at all, you've got big problems. You want your heat sink to be hot.
Anyone familiar with high end camping gear and has played with aluminum, titanium, and steel cookware can attest to this. Titanium is a terrible conductor of heat. Aluminum is one of the best conductors of heat. Titanium takes longer to heat up, but it also retains heat longer. Aluminum is an excellent conductor and heats up very fast, but also cools off very quickly.
There are three types of heat dissipation: radiation, convection, conduction. Radiation of heat is based on emissivity and reflectivity, and doesn't play a massive role here.
For conduction, carbon fiber has poor thermal conductivity compared to steel (though its much better than many other materials). Metals across the board are going to be much better thermal conductors 99% of the case. That is why heat sinks are usually made of aluminum or copper. There are exceptions to this general trend, but they don't concern us in this discussion. Keep in mind carbon fiber are strands of carbon thread suspended in an epoxy binder. Epoxy isn't the most thermally conductive material, and carbon fiber was never designed to be. Have you ever seen carbon fiber products specifically designed as heat sinks?
Convection is simply what it sounds like, using a liquid medium (in our case, air) flowing and carrying off excess heat. This can be natural (setting up convection currents on a static heat source) or forced, like air-forced cooling. This is why heat sinks have fins--to increase surface area and increase convection. Some argue barrel fluting increases cooling because of the increased surface area.
Also carbon fiber isn't necessarily stronger than steel across the board, only in specific applications and specifications (which widely vary with CF). Spider silk is stronger than steel in right applications. While carbon fiber can be made stronger in some aspect (strong as defined by...tensile strength? modulus of elasticity? etc) by weight, how much volume does a pound of carbon fiber take up compared to a pound of steel? Steel is much denser and might win out in some applications while carbon fiber is more suitable in others.
I know one issue I've heard of with machining flutes into a heavy barrel is that the mill work might change the size of the bore slightly. That's why they cut the flutes, then bore/ream so I've heard.
Tool deflection and any unrelieved/residual internal stresses on the material can lead to dimensional variations that don't appear "on paper". Metals also vary in composition from lot-to-lot. In aerospace, all the material dealt with is certified at every step starting from steel mills with a chemical analysis of the exact composition of a sample. Yet two identical steel alloys can vary one month to the next as far as how they react to machining tools, even if the analysis shows identical figures of impurities and alloying content due to so many other variables and factors. Every lot of material differs a little. Every heat treat differs a little. Nothing is 100% repeatable.