There have been threads, here and elsewhere, on this subject for some years now, and this type of barrel has gotten both good and bad reviews from the general shooting public.
I founded this company building lightweight, accurate sniper rifles for operational snipers, primarily military. I was a US Army sniper, and the point missed by so many others that were designing and building sniper rifles, and I think that was due to the fact that they had never deployed as a sniper, was that some poor grunt had to hump the **** thing in the bush, on top of the weight of his TO&E equipment.
This lead me to exploring the possibility of using carbon composite barrels as a component of our sniper rifles. We would be able to drop as much as 2 pounds off of the weight of what was already a lightweight design. The only drawback was that, up until lately, we were not able to get consistently Match Grade accurate carbon composite barrels.
My research into the subject lead me to Mike Degerness of Advanced Barrel Systems (ABS). Mike is the "mad scientist" behind the development of this technology, and his company holds a patent on their process which is different from the processes used by other companies who offer carbon fiber composite barrels. Besides being able to wrap a Match Grade barrel liner without degrading the inherent accuracy of the bore, the ABS carbon fiber matrix also increased the barrels ability to quickly shed heat (about 300% faster than steel). Logic tells you that a barrel that sheds heat that quickly will have a longer barrel life, and the empirical data so far, from Blackwater, is very encouraging. Blackwater installed ABS barrels in their 300 Win Mag sniper rifles and shot over 4,700 rounds (average barrel life for this cartridge is about 1,600 rounds) through them before replacing the barrels. The barrels weren't replaced due to loss of accuracy, but because the weapons were about to be sent over to the sandbox and new barrels were obviously installed. The barrels showed very little throat erosion and still had more, maybe a lot more, life left in them.
We got a number of them in .30 & .338 caliber and installed them on some of our magnum sniper rifles, and then fired a minimal 20 break in rounds (thoroughly cleaning between each round fired), and then started shooting them for record at 100, 300, 600, 800, and 1,000 yards. The accuracy was equivalent to our steel Match Grade barrels, and after shooting 20 round rapid fire strings with a Spartan MK100 338 Lapua Magnum rifle the protruding steel barrel tenon, the barrel, the receiver ring, and muzzle brake were only warm to the touch. In about 3-5 minutes the barrel was back to ambient temperature. Barrel fouling was minimal or about what you would expect from a barrel with so few rounds through it. We have been shooting these rifles almost continuously since we got them installed, and part of that is simulating operations in a target rich environment (shooting as many as 100 rounds in a rapid fire continuous string), and even under those conditions there was no degradation of accuracy which there would have been with a steel barrel due to heat build up.