It is correct to calculate the temperature stress at the maximum possible temperature the pipe will feel. If the line is long, long, long, as in a long pipeline, where there is a significant temperature profile, you should use that profile. In a plant where temperatures are usually assumed constant over relatively short lengths of pipe, and where temperatures are high, and where insulation is almost always used to keep the pipe temperature as high as possible and constant for the entire length, you should not use a profile temperature and take the highest of the maximum temperarure, or design temperature, or maximum design temperature, or whatever, for stress design.
If the process guys think the pipe might possibly get 500 degrees over normal operating temperature, and they have some reason to think that, like maybe they don't have a clue and its a WAG or whatever, use 500 degrees over normal operating temp. If you think they're full of it, then use normal operating temp. It's your decision ... and your responsibility, should you get it wrong.
Independent events are seldomly independent.