I will consider the problem of two quantum spin chains initially prepared at different temperatures, then put in contact and let evolve unitarily with a translation invariant Hamiltonian. I will focus on two examples: The XX spin chain, equivalent to a free fermion model, where the stationary states reached by the system at long times can be obtained by a variational principle, known as Quantum Action Method. Finally I will present a full ansatz for the non-equilibrium-stationary-state in the XXZ spin chain and compare its predictions with numerical simulations.