My first answer to anybody asking this question would be to give the data to a metallurgical engineer with the alloy number.
Of course he's going to be somewhat blunt, and probably make you a little mad at yourself for even asking the question. The term "cryogenics" is not new. Came into serious use during WWII, but now is kinda left in the shadows. Yes we still do it, but not all the time. Yet we now use it with non ferritic alloys now days. Still it has it's pluses (which I'll tell you about later). Believe it or not it was developed as a fast way to cold stabilize aluminum. They started doing this in freezers that would hold the parts (engine blocks for aircraft) for two to three weeks. Then somebody came up with a LOX and even later nitrogen that could be done in 36 hours.
When you heat treat a piece of metal (anykind), you are faced with a way to quench the heat treat (or to stop the heat). Yes you can do this via air, and with very low carbon steels this works well (think 8620 in a normalizing process). This does everything the cold process does, but with heat. Of course you can't do this with a hardened piece of metal. Why can't I normalize a hard piece of steel? (in our case a prehardened piece of steel) Because the heat process will draw the RC number back (soften it). With this in mind we will simply toss the steel in the deep freezer (nothing like the one in your house) and let it set there for a month or two. Otherwise we do the cryogenics process. I for one still think the slower process is better, but we also don't usually have 90 days lead time!
What do we want to get (results) out of cold stabilizing or cryogenics? I want to see the parts machine easier, and most of all change less during the process. The steel (in this case) is quenched via oil or water (I cannot by contract discuss the process in depth). In a perfect medium we want to quench the metal instantly all the way into the very center. Forget that idea!!! From the moment I dump that chuck of iron into the tank the whole world changers for the iron. Gets hard and develops stress points, but even six months later it's still going thru the quench process (bet a few here didn't know that!), and is actually changing three years later. Just they hand God dealt us. So now we have a piece of steel with some "retained martensite" (a form of granular structure that's not so good). How do I get around it? Best thing I can do is to dump it in the deep freeze (Cryo being preferred as it a much faster process, and time is everything in the quench process). The cryo process really helps the granular structure form correctly. Won't make a barrel last a shot longer, but it will do something. It will change less from the time it's cold to when it's heated.
To take this further; lets look at the stainless steel products that are so in vogue these days. 416 SS seems tobe everybody's favorite. Machines well, and can be bought prehard. (important). Barrel makers have their own special 416 recipe. Too many have an extra shot of Sulphur added, and that's not so good. They do this to aid machining and gain an increased tool life at your expense. Still remember that as the barrel heats up and then cools; it lets go of some items retained in the alloy. In this case it's Sulphur. Making the surface somewhat porous. The real bad side of 400 series steel is a little ditty called retained martensite. Now some guys are doing stainless in some exotic alloys that are quite a bit better. Think 15/5, 17ph4 re-arc met, and if your brave 18** numbers. These are well known to be hard on tooling and machinery. Still machined everyday by folks that know their business. With these you can be assured they have a cryo setup close by, and may use it as much as three times during machine processes. Makes it easier as well a much more stable. Yet all this will still not gain you one more shot.
gary