By using the framework of contact systems and thermodynamics it is possible to state the problem of matching an open-loop and a target vector field in an augmented space, where extensive and intensive variables can be seen as independent variables. This simplifies the partial differential equation associated to the solution of the problem and introduces the systems thermodynamic properties in the stability conditions when using Lyapunov's method. This is particularly useful for working with pseudo Hamiltonian systems, which arises when modelling thermodynamic systems. A control methodology is proposed and illustrated on a simple thermodynamic system. © 2011 IFAC.