I agree with Adobe to an existent. Most fluting is not deep enough to increase cooling surface area enough to matter. And again since it is so shallow the weight reduced is nearly un-noticable.
The most common solution to weight is to simple reduce barrel diameter.
I personally like big barrels w/ deep fluting. But the barrel has to be cryo treated after fluting to remove barrel warping stress, and it needs to be deep enough to make a differance.
This is why I've always been partial to Olympic Arms barrels, they are big .920 dia and they are fluted deep. Cooling surface area is probably doubled and my 24" fluted Stainless Ultra Match (SUM) is lighter than my buddies unfluted 20". Both shoot better than we can hold and once I shot 40rds as fast as I could pick up another ground squirrel and when done the barrel was simply only warm.
My
Hunt'nFish