I'm not sure about the solidification step of the simulation.
For solid materials that are simply assembled at a uniform hot temperature and cooled to room temperature, a simple Static Structural model can compute the thermally induced stress. I recommend you use SpaceClaim to create Shared Topology to eliminate the need for Contact in the model. Assuming the four solid bodies are in a single part file, click on the Workbench tab then on the Share button. You will see all the common surfaces and edges light up. Click the green check mark to accept this. Now when you bring this file into a Static Structural model, the mesher will create a congruent mesh connecting all four bodies with no need for any contact.
Constraining a face to be Y=0 is already an over-constraint on the geometry. For example, you would not do that to a bimetalic strip, that would prevent it from curving as the temperature changed.
The correct constraint is called a Kinematic Mount, which allows for strain-free thermal expansion of a body of uniform CTE. Here is a recent post on that topic.