It would help if you inserted some images to help visualize the geometry of the heat exchanger and the fluid domain(s).

I assume you will have both the fluid and solid domains in Fluent to have the temperature in the solid as well as the fluid.

You might not need transient structural because the velocity of the solid parts will be so low that there will be no inertia forces.

I think a Static Structural could be used, which includes the ability to solve with multiple time steps. The supports will be fixed at the initial temperature and so as the temperature rises, the material will expand and thermal stress will develop.