It would be interesting to actually run the calculations on how much better the cooling actually is on a fluted barrel. Unfortunately, I slept through most of my thermodynamics class in university and sold the textbook to buy beer.
My understanding of the barrel harmonics is that an odd number of flutes would be better. It has to do with the moment of inertia of the cross sectional area of the rifle, an odd number of flutes should have a larger moment of inertia, and therefore its stiffness should be increased, when two barrels of equal cross sectional area (and therefore weight) are considered.
Keep in mind I'm not a gunsmith, and this is based upon pure theoretical material mechanics (which I am also a bit rusty on). And we all know theory and reality can be two totally different things.