You are incorrect when you state that B31.3 requires that the design temperature should be used for analysis purposes!
The terms design pressure and design temperature pertain solely to pressure design requirements.
By coincidence they may end up being used in analysis but this may be merely coincidence.
B31.3 requires you to analyze the maximum displacement stress range. For piping attached to thermally displaced equipment it may very well be a lower ambient temperature whereby the pipes growth would not match the equipments growth.
I strongly suggest you buy one of the various references listed here
http://www.coade.com/support_reference.asp?varflag=Reference and in particular recommend the books by Woods, Becht, or Van Laan. It takes more than CAESARII to perform a credible analysis, the need for knowledge and experience can never be understated.