MR2005,
I don't want to create a big fuss. I endured a number of Heat Transfer courses in college engineering courses. Heat transfer theory doesn't support your last sentence above. Sometimes I wish I didn't know this ****...
The CF is an insulating shield to radial heat loss. The thin steel barrel will heat up faster than a thicker steel barrel - I agree. However, surrounded by the CF insulation wrap, the steel core of the barrel, thick or thin, will retain heat longer than without the insulating CF wrap.
Now, combine a thin walled steel barrel liner and wrap it with CF, and from a strictly heat transfer perspective, the steel core will experience higher temperatures for two reasons: 1) the thinner contour steel barrel/core temperature will rise at an increased rate per shot fired (because of the lesser mass of steel to distribute the heat across - less steel mass) and, 2) the steel barrel/core will cool at a decreased rate (because of the insulating CF wrap).
If I owned a CF barrel, I would be more concerned with steel barrel temperature than I would with a plain steel barrel. I would practice at reduced rates of fire. The only time I'd be banging away at a rapid rate, is if a wounded animal was getting away.
To my way of thinking, the only reason these thinner steel tubes with CF wrap barrels don't shift point of impact unacceptably through there faster heat ups and slower cool downs, is because the CF wrap is exceptionally stiff/rigid. This exceptional rigidity reduces the tendency of the steel barrel to warp during warm up cycles, such that they seem to shoot well - by most all recent reports I read.
If there's a heat transfer expert in the membership that wants to jump in here and identify the flaw in my post, please do. Open invitation... I don't expect anyone, or any CF wrapped barrel manufacturer's rep, will be able to dispute what I've just presented - at least not applying valid heat transfer science.
I'm not trying to say CR wrapped barrels don't or couldn't have some advantages. The advantages I see are reduced weight, better balance, increased barrel stiffness. I am stating they have no thermal efficiency advantages. They're worse than steel barrels, if we desire barrels that heat slower and cool faster.
For what it's worth. I've never believed the improved thermal performance marketing on and CR barrel. Any more than I've ever believed that some rifles shoot more accurately (better precision) at greater distances than they do at closer distances. It's that clear in my mind. Ain't gonna happen. Not until someone develops a functional miniature guidance system, implants it inside a bullet, and the bullet can self-correct it's flight path after it leaves the muzzle.