As someone who has had two rifles built with fluted barrels and uses them in competition, here is my take on this. Fluting should only be done on cut rifled barrels prior to reaming the barrel, which is done just before the barrel is rifled. Any change to the barrel contour after the rifling has been done CAN have an impact on the bore dimensions. Why have a barrel fluted? Aside from the aesthetics, the only reason, IMHO, is to reduce the weight of a heavy contour barrel to better balance a rifle or have it meet weight in some form of competition. Forget about the cooling faster thing. My barrels still need a long, long time to cool down after a string of 30 shots over 30 minutes.
Don