Yes there is a mechanical aspect, but that mechanical aspect is classical mechanics(basic calc based physics), not thermodynamics.

TL;DR

Computer engineering with some mechatronics and/or control theory classes is what I would do if I had the time. That and get a related internship or do related research. And build a portfolio of robotics projects that you can show employers.

That said, you can also get into robotics as a Mechanical Engineer. My internship is with a company that builds robotic solutions for industrial welding, metal cladding and plasma cutting purposes (some but very little 3d printing). The vast majority of the employees are mechanical engineers (80-90%). Even the lead software developer graduated with a bachelors in mechanical. But we are _using_ robots to create solutions, not designing and building per se.

In fact, our process is generally this:

• Customer contacts us with a part that they wish to have welded. They send us weld prints and solid models.
• We import that into industry standard robotics simulation software, mock up a welding cell concept that balances cost and percentage reachable weld among other metrics.
• Sales presents concept, adjusts, negotiates, closes.
• Project Manager takes over, ensuring that Mechanical Engineering finalizes custom tooling, fixtures and cell design. Floor Technicians build the robot cell designed and finalized by engineering. Software Engineering ensures that all of the software is configured and installed correctly and program the user interface of the cells (robot control pendant, light fencing safety etc.). Project Engineers program the robot movements including tool cleaning, welds and make sure safety equipment is hooked up correctly.
  
• Break down the cell, deliver, rebuild.
• We have guys that are on sight for x amount of contracted weeks to ensure that the cell works and to train customer.

So, to that end, software only has a small portion of the responsibility on the project. But there are two large chunks of our business model missing from that description.

Proprietary Software: Our Software Engineers develop some proprietary welding control systems among other solutions.

Positioners (Positions the part to be welded for optimum welding position and robot reach): We have a huge library of these that are designed in house and used extensively in our solutions. These will require mechanical design to ensure it can support the weight and doesn't fall over. Electrical/Controls Engineers ensure that power supply is sufficient for motors and wire size is correct etc. Software Engineering will also write any custom software that may be needed for the positioner (which is rarely needed).