Though graphical representations of numbers were widely spread in the mid-19th century, physicists struggled to extend these to the third dimension. Unruly materials, lack of instrumentation and reduced accuracy have generally discouraged the use of three-dimensional models for quantitative rather than just qualitative analysis. This talk will show why thermodynamic models (i.e. three-dimensional representations of the variation of quantities such as pressure, temperature and volume) flourished at the end of the 19th century despite such challenges and drawbacks. While the graphical manipulation of curves on paper was part of formalized disciplinary practices (descriptive geometry, graphical statics etc.) and relied on well-established instruments (autographs, planimeters, drawing instruments), the construction of three-dimensional models was carried out through a bricolage of techniques and informal tinkering. Thermodynamic models could be constructed by joining sections of wood (according to the methods followed in a shipbuilder’s modelling-room), or by moulding a plaster-cast. Some physicists, like James Clerk Maxwell, traced curves of equal pressure and temperature by placing the model in the sun light such that “the rays just grazed the surface”, or would “spread a film of grease on a sheet of glass and cause the sheet of glass to roll without slipping on the model”. While engaging with the challenges and drawbacks encountered in the construction of thermodynamic models, this talk will focus not on the objects, but on the movement between one media to another. It will be shown that the thermodynamic models were neither alternatives nor simple complements to paper diagrams. Instead, their role and value were given by the ease with which one could move from paper to model, and then back to paper.