Your question isolates stiffness as a criteria.
That can be checked . Any number of setups will accomplish the same thing,
Use a repeatable load (a weight) and a dial indicator to measure deflection.
That will measure stiffness.
As far as heat..depends on what you are doing. If you are shooting slowly and waiting for a particular temp,the additional surface area may help.
But a small team trying to disengage with massive fire ,one full auto mag dump after another, will find the barrel mass of a non fluted H-Bar will soak more heat than a fluted bbl. Its a mass thing.
Accuracy? I'm sure there are examples of finished barrels that were then fluted that shoot very well.,and smiths who will say "I've been fluting barrels for 20 years and they dah....dah...dah.... OK. I'm not there.
I can be skeptical.
IMO,the fluting should take place early in the barrel making process,and stress relieving ,then rifling and lapping. I'll leave that to the barrel makers to define,Its probably different for cut rifled vs button rifled.
No machining cutter is perfectly sharp. They may largely cut chips,but to some degree,steel gets beaten and displaced, The effects may be infinitesimally small, but I would guess fluting a barrel would make the bore grow in dia,be less round,less straight,and rubber band like stresses would be introduced.
That they still shoot may be largely about the unfluted section at the muzzle that says "goodbye" to the bullet.
I have nothing against fluting. I agree weight for weight,a fat fluted barrel will be more rigid than a skinny unfluted barrel.
But,IMO,fluting should not be an afterthought add on. I want it designed into the barrel making process by the barrel maker.
Something I know nothing about: How the barrel is "tuned" in harmonics,where it will flex,where it is rigid,where to place mass, all figures into the accuracy.