I've retried yesterday and it works but you have to specify, also in thermal mode, a contact region between pieces since you have a contact region in structure mode.
You shouldn't need to go into the thermal mode to do this; the structural side of Mechanica was a thermal load that you can use.
The problem is the good design of the link of the beam (points) with the solid geometry, so you have to make some surface regions and rigid links.
Correct, although you can also used weighted-links (avoids the singular issues with rigid links).
I've done a little simple model for analyze the differences between a model modeled with a fastener and a link made with beam.
There are differences around the link, caused by the rigidity of the link (I've put a rigid link); from here the importance of the design.
Try a weighted-link; this will prevent the infinite stiffness discontinuity. At the end of the day, regardless of whether you're doing it with beams or with Mechanica's fastener tool (which uses a network of springs), you're creating a linear representation of something that is very non-linear.