In the first part of this lecture we will introduce the notion of contact Hamiltonian systems and their dissipative properties. In the second part we will apply this formalism to the study of thermodynamic systems. Indeed, by means of the Jacobi structure associated with a contact structure, we use the so-called evolution vector field to propose a new characterization of isolated thermodynamic systems with friction, a simple but important class of thermodynamic systems which naturally satisfy the first and second laws of thermodynamics, i.e. total energy preservation of isolated systems and non-decreasing total entropy, respectively. We also consider more general kinds of thermodynamic systems, which are described by at least two thermal variables and exchange heat between its components.