Here is some of that "play on words" thing I was referring to....you could say that hot gases DO NOT conduct anything, hot gases are present and the surface of the bore tries to reach an equilibrium. I believe there is some scientific law regarding this action. I apologize for my current inability to quote it. Every element has a thermal number, the hot gas being the "source" to heat the barrel steel we are not concerned with it's thermal number...we don't care how long it took the heat to go thru the gas itself. Maybe a better way of saying it is that the temperature of the gas is not the problem, it how hot the steel gets that is.
One would hope fluting the OD has no effect on the bore...if it did then certainly no one in their right mind would pay to have it done!!! You are correct {at least I think so} that fluting has no effect on thermal transfer through the barrel wall itself, but it very definitely affects the outer surfaces ability to dissipate said heat once it gets to the surface....again, think of radiator fins. All this is of course given the fact that we have functional flutes and not just cosmetic ones. Flutes or other heat dissipating enhancements aside, there is also this matter of mass itself...a 6 pound piece of steel, no matter the thermal number, will always take longer to cool than a 3 pound piece.