Vick,

In my opinion,
The B31.3 "design" temperature (and it's coincident "design" pressure) is only used to set the minimum wall thickness.
If I am performing a structural (or stress) analysis of a specific, say, operating "state" of the piping system, I would set my pipe temperature to the metal temperature of the pipe. Para. 319.3.1(a) provides an example with the statement "Values of thermal displacement ... for computing the stress range shall be determined [based on] ... maximum metal temperature and ... minimum metal temperature for the thermal cycle under analysis." There is no mention of "design conditions" here.
Use your line list.
(Here's where things can get sticky ...) Many systems have a higher design pressure/temperature pair than the actual operating pair. Does this mean that an operator can arbitrarily increase operating conditions as long as they remain below design? I'd say yes if the only concern is maintaining the pressure boundary (that wall thickness rule). But this wall thickness concern does not address changing support conditions which may lead to collapse (SL > Sh) or the fatigue life of the line (SE > SA). This is one reason why engineers analyze the "design" conditions - to be sure the system is safe under those (possible?) loads.