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I was in the process of typing a detailed response regarding the thermodynamics, heat transfer, and materials science processes at work with what you are proposing, but aborted due to the late hour.
The gist of it is that it is highly unlikely that you will cause microstructure changes to the material itself unless the barrel is glowing red hot, but you will almost certainly induce dimensional changes due to the localized accelerated temperature change. This is fundamentally a bad idea.
But since a barrel heats unevely does cooling unevely really matter?
DevL, you are correct that the barrel does indeed heat up unevenly, but assuming that it is symetric in cross section at each point along its length, the disparity would be in the longitudonal direction rather than radial. As the thermal conductivity of carbon steels is quick good, thermal equilibrium is pretty rapidly achieved along the length. As we all know, one can heat up a barrel very rapidly.
Considering that the thermal expansion coefficient for carbon steels is on the order of 10^-5 in/in/F, one could expect a 16" barrel to theoretically grow in length 0.160" at 1000F. The corresponding radial growth would be 0.002" for a 0.750" diameter barrel with a .224 bore.
The problem with what the OP is proposing is that the propellent used in "canned air" is a gas at atmospheric pressure, but a liquid when pressurized. When the liquid is released, it experiences a phase change extremely rapidly, and the associated heat of vaporization is substantial. The expected irregularity of application would tend to be in the radial plane, with corresponding localized "bending" of the barrel so induced.
You have watched me pour bottled water on our cans to cool them down more quickly. The difference is that fluid is a liquid at atmospheric pressure, and vaporization is much slower and correspondingly evenly distributed as the water covers the entire surface of the devices.
As a practical experiment, pour some ambient temperature water on your hand....no wahalla. Then spray some "canned air" on your flesh, and it will get "frostbite" when the water in the cells immediately freezes.