"IF" the temperature does not exceed the critical temp, which varies a bit according to the amount of carbon in the steel it does not Harden, Period. In fact, it will draw/temper the hardness which was put in when the gun was built. An action can be "Colored" below that temp, but you w2ill lose the case hardness & only gain the color. Case Hardening, technically known as Carburizing does indeed harden the surface, "The Case". It does take the sudden cooling to affect the hardening process. When the critical temp is reached the molecules in the steel are re-arranged & the part also becomes Non-Magnetic. The Quench "Locks" the molecules in their new position, if it colled slowly they would go back to their original position & you would have Annealed the part.
If you get the part hot enough to color but below that critical temp, then the hardness is as I said tempered out & you have lost that hard case which was present. As I said I was not a heat-treater, but have seen it done in the machine shops I worked in, though in these cases it was done for the effect, not for color. Parts normally came out a grey. They were "Always" quenched in either oil or water. Some form of animal charcoal is used in color hardening, to obtain better colors.
I will agree it is not a Backyard project. If one insists on having it done send it to someone who is very well versed in the operation, & also do not allow it to be simply re-colored without re-hardening. Me, I will live without the color rather than risk damaging a gun that has not been made for many, many years. The original makers likely allowed for some number of failures.
In my 35+ years in machine shops I never saw a part go through heat-treating of any sort, either through or Case hardening which "Did Not Move" by some amount from the configuration which it had prior to being treated.
Take it for whatever its worth to you or totally ignore it. It's your gun, not mine that'll be exposed.
