Just for the hell of it, I looked up the properties of 416 stainless and 4140 steel to see.
416 has a thermal conductivity of 24.9 W/(m-K) at 100C, while 4140 is 42.7 W/(m-K) at 100C. This means that the 4140 will conduct heat through the material at 1.71 x the rate of the 416. This means the C-M barrel will move heat away from the bore 1.71 times as fast as the SS. The end result is not at all linear, because the overall heat transfer to the atmosphere is dominated by the interface between the barrel material and the air.
416 also has a specific heat capacity of 460 J/(kg-K) and the 4140 is 473 J/(kg-K), which means that it takes slightly more energy (473/460 = 1.03 times more) to heat the 4140 up any particular amount.
So, I guess there is some validity to the idea. Whether it makes a practical difference when out shooting, I don't know.
Mark
