AI did extensive research on fluting barrels. They used high power precision lasers on fluted and non fluted rifles.
In a nutshell, their research showed that the unequal heating and cooling caused by fluting was detrimental to accuracy. Especially where there is barrel area covered by stock surface, even if properly beaded and free floated.
I don't recall the total amount of POI change from uneven heating, however it was enough that AI quit and no longer produces fluted barrels because of their concern for accuracy.
Their conclusions were use non fluted barrels.
I can say from personal experience the Proof barrels do work as advertised, especially at extreme ranges. Buy once, cry once.
Bartlein barrels put out a blog citing the AI research (I can't find my old link to the full AI procedure, testing and results).
From Bartlein publication -
One design change that resulted from AI's exhaustive accuracy testing and development of the PSR [Precision Sniper Rifle] is the removal of flutes from the barrels. Engineers at AI decided to isolate the barrel flutes to see what impact they had on accuracy. The engineers attached a laser to the rifle's receiver, another to the barrel, and a third to the scope. All three dots were zeroed at the same point, then they started shooting the rifle. They discovered that, no matter which fluted barrel they used, the dots would diverge as the barrel heated. The dots from the devices mounted to the scope and the receiver would stay in place, but the barrel's device would manifest a point-of-impact (POI) shift. The POI shift from the warming barrel greatly diminished when they used barrels without flutes.
Engineers determined that the flutes never heated evenly, causing the POI shift. I hope the results of this test gain wide circulation through the sniper and long-range shooting communities to help eliminate some of the ignorance that surrounds the perceived advantages of barrel flutes. Flutes are great for shaving weight, but this is the first test I've heard that provided empirical data detailing what happens when the barrel is fluted. This should be the death of the "they cool a barrel faster, so they're more accurate" argument, listed among flutes' virtues. Our goal is and should always be to mitigate the effects of heat; fluting exacerbates it.