Contrary to popular opinion CF is just about the exact opposite of most I've read here. It is highly resistant to effects from heat. It can withstand temperatures over 2500 degrees, does not warp. and absorbs and dissipates heat much faster than steel. It's use in brake systems and clutches has been well vetted.
It's benefit to rifle barrels is debatable, unless someone figures out how to make a complete barrel from it.
BTW, the M60 has stellite lined barrels and is not that hard to burn one up,
What you say is true about carbon ceramic brake discs, which have about as much to do with carbon wrapped gun barrels as does a big Tiffany diamond ring. Yes, carbon is involved in all three, but they are not all the same...... not by a long shot.
Carbon fiber is attractive because it has a VERY high modulus meaning when you pull it it doesn't stretch very much. That means, assuming you apply it in exactly the correct way, it can be made into components which are quite stiff. Since it's also pretty light and pretty strong, these components can also be light and strong. But they're not automatically light and strong. You gotta' design and fabricate the component with great care to realize the advantages of carbon fibers.
Carbon brake discs are made by molding chopped carbon fibers with a plastic resin which is later cooked at high temperature turning the binder into carbon too. Then Silicon is added to the mold and the component is heated to an even higher temperature to produce Silicon Carbide. After machining the discs are really not much like the original two components other than the chopped carbon fiber strands are still in there to provide strength.
Carbon wrapped gun barrels, on the other hand, are usually made by wrapping carbon fibers, either as linear strands or woven cloth, around a steel liner. The carbon fibers are encapsulated in some sort of resin either as it's being wound or perhaps pre-impregnated. Later that resin is cured by heating, but at much lower temperatures that that used to make carbon ceramic brake discs. The finished product is similar to your ordinary fiberglass boat except that the fibers and resins are higher strength. However, the basic idea is similar. Both use a strong fiber bound in a resin matrix which can be easily formed and then later cured to make a stable finished product.
Keep in mind that carbon fiber is highly anisotropic, meaning it's properties vary, often significantly, depending on the exact orientation of the fibers. In addition, the resin has a great deal to do with the properties of the finished product including thermal conductivity and these properties can be adjusted to suit the requirements of of the finished product.
It is possible to make a carbon fiber wrapped barrel which is lighter than a heavy steel barrel while also being equal in stiffness. However, some tests show that heavy steel barrels show less POI shift as they heat up compared with carbon barrels. It has also been shown that it's easier to aim with a heavy barrel than with a light one, so all is not sweetness and light. Are you gonna' carry the barrel as you're chasing bad-guys (or Gods little furry creatures) around or rest it on a bench and shoot it for score?
The jury is still out when it comes to carbon barrels. They may be the wave of the future, but it is unlikely they will be cost competitive with steel barrels anytime soon. Me? I'm sticking with steel.