I don't think cryo treating is always the answer, depends on the steel. Some barrel makers do temper their barrels (stick in an oven at prescribed temp. and soak time) to relieve stress so I don't know if I agree with heating a barrel up during shooting would cause any inherent stress to raise its ugly head unless there is uneven heating of the steel causing expansion at different rates/places.
My theory on the subject has more to do with the contour of the barrel( all else being equal). A barrel with an exterior parallel to its bore, or close to it, such as the original military Mauser step barrels expand with heat more uniformly than continuously decreasing radius sporter barrels(obviously the thicker the barrel the less this effect occurs). Throw in the insulating effect of the stock on the bottom half of the barrel and you get the top dissipating heat faster than the bottom, possibly the cause of vertical string and the like. Again,just my theory which has not been tested and I'm no scientist, so take what you want from it.
