Heat Transfer
Get ready to be blown away. There is another misconception about fluting in relation to cooling the barrel.
Some people believe that fluted barrel cool off faster than regular barrel because the surface area of a fluted barrel is greater than a plain one. I am sorry to say that this is absolute fallacy. Fluted barrels indeed cool off faster than a plain barrel of the same diameter, and not because of surface area, it is because of other factors.
Here's why:
Let us say you fire 10 rounds in 10 seconds in a hunting rifle. And at the same time your friend also fires 10 rounds in 10 seconds in a bull barreled varmint rifle. We all know that heat is generated as a result of the bullet going through the bore at a high rate of speed, causing friction and releasing energy. Now, the temperature inside both barrels should theoretically be equal, but the temperature on the surface of the hunting rifle will be a lot hotter than the temperature on the surface of the varminter. It is because the wall of the hunting rifle is a lot thinner than the wall of a varminter. The closer you are to the heat source (the bore of the rifle) the hotter it is on the surface of the barrel. Makes sense? In essence, the thickness of the barrel acts as an insulation. In short, the thinner the wall, the faster the heat reaches the surface and the faster the heat will be dissipated into and equalized within the ambient (outside) temperature. This type of heat transfer is called conduction (the other two are convection and radiation).
Here is an excellent analogy. We love to barbecue in the summer. Place an aluminum foil on the grill to cook you burgers. After you burgers are cooked, remove the aluminum foil and notice that it cools off almost immediately. Now fold the aluminum foil to make it thicker and put it back on the grill. Remove it afterwards and you will notice that it does not cool off as fast. It is the same analogy with barrels. In short, hunting rifles dissipate heat quicker than varminters do.
So how does fluting aid in heat dissipation? Basically, as materials are removed the flutes become closer to the bore. So when the bore gets hot after firing several rounds, the heat generated reaches the surface of the flutes a lot faster than a plain barrel of the same diameter.
Conclusions
In conclusion, a regular plain barrel is a lot stiffer than a fluted barrel of the same outside diameter; however, a fluted barrel is a lot stiffer than a regular barrel of the same weight. Fluting will definitely dissipate heat quickly. And it is not because the surface area is increased; it is because the heat is allowed to reach the outside temperature at a faster rate by removing materials. If your bull barrel becomes unbearably hot on the surface, it is safe to assume that the bore temperature is at a point where it can literally dissolve soft materials. This will damage your bore in the long run.
So if you wish to flute your barrel, it should be because you want to reduce the overall weight of your rifle and you want your barrel to cool at a faster rate. Fluting your barrel with the belief that it will add stiffness just doesn't make any scientific sense.