One commonly and persistently difficult topic in thermodynamics is the relationship between the different thermodynamic potentials obtained through Legendre transformations. The Partial Derivative Machine (PDM) was developed at Oregon State University to be a mechanical analogue of a thermodynamic system. This analogue allows students to explore the mathematics of thermodynamics, including Legendre transformations, on a mechanical system that students can understand without having to first learn new physical concepts. We conducted 12 teaching interviews with middle-division undergraduate physics majors to explore student usage of the PDM. In these interviews, we taught interview participants Legendre transformations on the PDM and then asked them to perform a thermodynamics transfer problem. We found that participants used the PDM productively and in different ways while performing the transfer problem. Furthermore, many participants stated that the teaching interview helped their understanding of Legendre transformations.