In this thesis, we consider heat-conducting chains and networks, which are prototypical examples of non-equilibrium systems. We prove the existence and uniqueness of an invariant measure (also called non-equilibrium steady state) for some classical systems made of interacting oscillators and rotors coupled with stochastic heat baths at (possibly) different temperatures. We start by introducing the models of interest and putting them into context. We then focus on the uniqueness problem for networks of oscillators, by introducing a set of tools to verify Hörmander's bracket condition. Next, we prove the existence and uniqueness of a steady state for chains of 3 rotors. We show that the system converges to this steady state at a stretched exponential rate. Finally, we extend these results (existence, uniqueness and convergence to the steady state) to chains of 4 rotors, which requires to deal with resonances.