Using your terms (OPE-SUS) will equal T alone in linear systems. Nonlinear supports (typically vertical) complicate things.
Here on earth, gravity has the pipe resting on the support when it is cold. As you add thermal strain, the pipe most first overcome this deadweight load before any movement occurs. And the final position of pipe will incorporate that deadweight sag along with the thermal strain.
The piping codes are quite clear in their fatigue evaluation - it's a range of displacement. That's why we use (OPE-SUS)

Think of your T alone as an analysis in outer space - no gravity.