I have shot a couple or three fluted barrels that a buddy has and have the opinion that fluting doesn't affect the performance noticeably. The barrels are all Ron Smith barrels and I think Ron has all his product stress relieved after drilling, reaming and rifling but before contouring or fluting. The one rifle I have shot I think was the first foray into fluting for Ron... and being a farmer, he called it a PTO shaft rifle.
Personally I have a couple of octagon'd barrels, one done by myself and another done by another "hobby" machinist, both were done with light slow cuts so as to not generate a lot of heat build-up in the barrel blank, neither one has been heat relieved after machining and both shoot P.C.'d cast into almost an inch.
My point being is that a commercial shop that has to get a job out as fast as possible might generate enough heat in a blank to cause heat warp but if a barrel is done slow & easy then I doubt it will make any difference to normalize the steel. Another fact not mentioned here is that 1000's of barrel blanks have been bought from manufacturers and contoured at gunsmith's around the world without any thought of stress relieving after contouring and fluting is just another "removing metal"machining process the same as contouring.