In my opinion, there's no difference in accuracy between two match grade barrels with the same bore and chamber dimensions but one thicker than the other. While each one will have a different resonant frequency it whips at when fired, it'll always be the same frequency and amount for every shot fired. It doesn't matter how much or how fast it wiggles; it's the most repeatable thing from shot to shot in a rifle-ammo system. I've not observed any difference in accuracy between my own stiff and whippy barrels. The basic reason why match barrels are thicker and heavier is they make the rifle hold more steadily in shooting positions. More mass held by us shooters moves around less while we're aiming.
Nor have I and others observed any change in accuracy in match barrels properly fitted to receivers as they go from ambient temperature to way too hot to touch. Barrel heat does not change the resonant frequency they whip at. At least not until they get soft and rupture when fired. Folks shooting prone match rifle matches have 22 minutes to shoot unlimited sighting shots and 20 record shots at 600 yards. At 1000 yards, they have 30 minutes to do the same thing. Some of them will put 5 or 6 sighters down range before their 20 record shots and only make sight changes to correct for changing cross winds. Accuracy does not suffer and impact doesn't move around.
Starting with a cold barrel, I've put 30 rounds down range to a 1000 yard target testing a 30 caliber magnum in 20 seconds; all 30 went inside 5 inches. I forgot to bring my IR temperature gauge to measure barrel temperature, but I'd had a bad 2nd degree burn had I laid that barrel against my neck.
A friend had his .308 Win. match rifle clamped in a machine rest and fired 40 shots about 20 seconds apart at the 600 yard target. The barrel was cool at the start, but all bullets went inside 2 inches down range. That barrel was really, really hot when the last round was fired.
Lake City Army Ammo Plant tested 7.62 NATO match ammo shooting a couple hundred shots 20 seconds apart in their test barrels. With good lots of National Match ammo, all of the bullet holes would fit well inside a 6 inch circle. Pretty darned good for new cases, metered powder charges, and MIL SPEC chambers.
Virtually all factory barrels are fit to receivers such that they bear hard at one point around their tenon shoulder; that flat part that touches the face of the receiver. That happens 'cause the receiver face ain't square with its threads for the barrel. As the barrel heats up and expands, it bears harder at that point and it wiggles differently with more pressure at that point than all the others around it. Squaring up the receiver typically fixes that. Match rifles properly built have receivers faced square with the barrel threads and chamber so they won't change point of impact when they bend from getting hot.
The only difference between a match and standard barrel is typically the tolerances of their chamber, bore, and groove dimensions and twist. This has no effect on how their accuracy changes as they heat up.
Here's a link to barrel temperature tests on an M16 rifle that's interesting: