Pete,
With all due respect, I must disagree. As you shoot a rifle the barrel will heat up. If the barrel is not symetrical I would expect the heating will cause the barrel to bend toward the thinnest side.
Maybe so. I do have a late percussion with a 15/16" 36 cal gain twist that is built as I described, however. The small caliber, heavy barrel and gain twist all make me think it was built more for shooting than hunting, though. I hadn't really thought about the fact that the swamp may cause something weird to happen, although I would think the uneven heating would also happen in an assymetrical barrel whether swamped or not.
All barrels are subject harmonics. From the time the trigger is tripped, every subsequent action (hammer, frizzen, firing pin, ect) from then on produces additional vibration reactions in the rest of the gun; particularly the barrel. When the cap, primer and/or main charge ignite, each produces its own unique set of annular pressure waves in addition to the vibration waves that are already running the length of the barrel. Both the annular pressure and the vibration waves are affected by exterior influences such as pressure points created by the stock, anchor points and such things as where the stock/barrel is placed on a rest as well as the amount and manner of pressure that is applied. It doesn't matter if the operating pressure of the load is 65,000 psi or 6 psi, any level of rapid pressure change will create annular pressure waves just as any movement or impact will induce vibration waves. Residual stress in the barrel will also affect the manner in which the annular pressure and vibration waves traverse the length of the barrel.
All barrels are subject to at least some degree of un-even heating/cooling. The stock material is both an insulator and air dam that serves to hold the heat in the barrel and prevent the free-flow of air around the barrel. Any temperature differential within any barrel has the potential to cause barrel deflection; additional factors like residual stress and lack of symmetry compound the issue. Even a barrel that is fully heat treated and stress relieved will still warp from temperature differentials because hotter/cooler areas expand/contract more. With all things being equal, a perfectly symmetrical exterior profile of any shape will not have a definitive cause to warp in any given direction provided there is no temperature differential. A barrel with one side thicker than the other will tend to warp towards the thinner side as it is giving up heat energy quicker and thus not expanding to the degree the heavier side will. A perfectly symmetrical and stress-free barrel having the bottom half covered with stock or other insulating material will normally warp upward as the very top will shed the heat energy quicker.
One something like a SxS or O/U arrangement and continually firing just one barrel - the initial warping will be from the non-attached side to the attached side until the temperature differential shifts and the attached side attains and retains more heat energy than the non-attached side.