2p, thanks for the reply. Here are some comments.
You have brought up a point which needs to be understood by all contemplating having this done. This is the fact that a carburizing cycle "Changes" the composition of the outer layer (The Case) of the steel. Indeed the depth of the case is controlled by how long a part stays at temp in the carbon mixture. Every time it goes back in the furnace for further heating a little more carbon is added to the case. Thus every time a part goes back in the furnace it will be slightly "Changed" from what it was previously in actual composition. A craftsman who understood the "change" issue could make a rehardening cycle very short and without a carbon rich environment and still have a hard case. Thus, you would restore the hardness to the case with a minimum of change in case carbon content or depth. Even alloy steel can experience a slight compositional change in heat treatment from certain alloying elements "Cooking Out" of them, from oxidation. These steels are often heated in a molten salt to minimize this. I agree that cooking out and cooking in (usually carbon) alloying elements are issues. Anyone can do a simple case hardening of a simple piece of mild steel. Gun actions are not simple pieces, not at all. Therefore, I will always suggest that gun actions that are to be recased are done only by craftsmen.

The problem with the color case hardening is we cannot simply heat enough for "Just" the color without destroying the hardness of the case, & we cannot process in such a way as to preserve its hardness with out going up into the range where more carbon will be absorbed & the part then be quenched from above its critical temp, which is almost certain to result in "Some Amount" of dimensional change. Certainly recoloring without tempering out the hardness of the case is an issue. Dr. Gaddy thought it paractical. But, I can't yet cite the metalurgy to do it. A careful study of hardness vs temper temperature would need to be made (the higher the temper temperature, the lower the hardness and brittleness). If rehardening, there is no need to soak the piece above critical temperature - reheat and immediately quench will produce full hardness (core temperature is not an issue as it will not heat treat under any circumstances, only surface temperature). Nor is there any need to expose the piece to additional carbon. So, we can see a method to minimize ally changes. There remains the issue of minimizing dimensional changes due to the heating and cooling.
To me the Risks are simply not worth it for a little Vanity for the colors. The proper original hardness of the case itself has not been lost, only the color. [/quote]

In my opinion, and it is only an opinion, most guns can be refurbished to a very acceptable level without recoloring. However, when one is to be fully restored, made as near new as possible, then recoloring is in order. My caution is that recoloring, including rehardening, is not a step to be undertake lightly. A recolored action on a refurbished gun looks out of place. However, a "silver" action on a restored gun also looks wrong. One needs to understand the difference in work and cost between a refurbishment and a restoration.