It's referred to as "thermal bowing" in CAESAR, and is in the special execution parameters. Though I've never had to deal with it, personally.

Offhandedly, I'd say if you know the temperature difference and OD, you can estimate what radius R would be the resulting bow.

You could then turn the curvature into a displacement and rotation of the end, though if it's something you can physically see in the field, there's a chance you're outside of CAESAR's "small displacement" applicability.