Any inset i.e. fluting will not give you any great additional rate in barrel cooling. Conductive and radiative modes of heat transfer with the normal amount of additional surface area give no substantial benefits.
If your willing to give up a certain amount of rigidity for weigh, it works. Any added benefit of cooling is poor. The detrimental effect of poorly machined barrel flutes are of greater significance. Any error in length, width, and depth of the individual flutes will cause different expansion rates in the barrel. They already do as in post front site application where a relatively large thermal mass suddenly meets a low thermal mass. However any barrel deviation should cancel out if they are machined equally.
Any added benefit of rigidity, strength or accuracy is pure hype.
If there is any application where is would be of benefit, it would be in a non-target semi-auto lightweight configuration. Fluting a >9lb bolt rifle with a heavy barrel is pure nonsense. My stance is if you want a lighter configuration get a smaller barrel profile.
They are not "very strong" in any application, you are sacrificing strength for weight. I give you that a fluted barrel is stronger PER WEIGHT (more or less given the axis) then the same mass, which would determine a smaller O.D. In the same time you are adding higher order barrel harmonics and an increased chance of a non-uniform machining.
If it were not for the high tech look, which manufactures play off of, the fad would have disappeared long ago.