Any time a piece of steel is heat-treated, either case hardened or through hardened it does indeed go through heating to above its critical temperature & then a sudden Quench in some form. In case hardening this quenching medium is normally oil or water, depending upon the exact composition of the base metal.
There are what is known as Air-Hardening steels & also Precipitation Hardening steels, particularly in the stainless line. Neither of these latter are used much in gun-making.
While I was NOT a heat-treater nor an Engineer, I have seen many parts go through heat treatment. Personally, I would never subject an older gun of mine to be Re-Case Hardened. The original hard case is still there, all you gain is cosmetics.
You gain cosmetics at a considerable expense & run the risk of warpage or even a cracked frame. In many cases, we do not even know for certain what the exact alloy of the frame is. Sure we know it is a comparatively mild steel, but even then differing amounts of carbon content & other trace elements can affect the outcome.
I am absolutely amazed that British proof law would not demand re-proof after a re-hardening.