On Stacked Exchangers intermediate saddles are modeled as rigid elements.
However there are also process(pipe) connections that connect upper and lower Exchanger.

The process connections are at higher temperature compared to the saddles because the saddles are exposed to atmosphere.
How the differential expansion is accounted for? About 2-5 mm differential expansion would cause large forces, however in the real application there haven't been any complaint from the Field and they seem to work fine, flanges do not leak.

How would you normally calculate the temperature of the saddles for a given operating temperature of the Exchanger shell so that co-incident temperatures can be entered in a Stress Model?