Hello,
The B31 Code that was going to be the cryogenic piping Code would have been B31.10. However, that committee decided that it was so much a parallel to B31.3 that they recommended that it be folded into the B31.3 Process Piping Code (this same process happened to the would-be B31.6 Chemical Plant piping Code - it was also folded into B31.3). There are some special considerations for cryogenic piping but for the most part they center around material selection.
The B31.3 Code was reviewed and changed where appropriate for cryogenic piping design to include special consierations for material ductility, fabrication and testing. The topic of cryogenic piping design is now adequately addressed by B31.3.
With that as background, it is easy to see that B31.3 has the broadest scope of any B31 Pressure Piping Code. That is why the B31.3 committee created rules for various "fluid service categories" (category "D", "M" and "normal service"

. The idea is that within B31.3 there should be a degree of rigor (for design, fabrication, erection and testing)that is appropriate for the severity of service and potential risk.
Cryogenic piping is the prime example of systems where the "operating temperature" is lower than the "installed ambient temperature" (at ambient installed temperature, the piping is essentially "stressless" when only displacement (expansion/contraction) stess is considered. So when calculating the displacement stress range, the range of temperatures from the hottest (maybe "out-of-service" on a hot summer day) to the design operating temperature (coldest) is used. A departure from the more frequent case where the operating temperature is the hottest temperature (with the exception of off-design upsets)and ambient ("out-of-service" on a cold winter night) is the coldest temperature.
Bottom line, use B31.3 but pay attention.
Best regards, John