Don't get too concerned by all the T1-T2 stuff. That is for the user to sort out.

B31.3 is quite clear on this.

For example, in a typical high temperature system, installed at a moderate temperature but subjected to a low winter temperature, the stress range will be the algebraic sum of the installation to high temperature stress and installation to low temperature stress. Other cases will be needed for equipment and support loads etc.

If the installation to low temperature part of the stress range has been ignored, the calculation is simply wrong. Maybe not by much, but still wrong.