  We employ the Quench Action Method (QAM) for a recently considered
geometrical quantum quench: two free fermionic chains initially at different
temperatures are joined together in the middle and let evolve unitarily with a
translation invariant Hamiltonian. We show that two different stationary
regimes are reached at long times, depending on the interplay between the
observation time scale T and the total length L of the system. We show the
emergence of a non-equilibrium steady state (NESS) supporting an energy current
for observation time T much smaller than the system size L. We then identify a
longer time-scale for which thermalization occurs in a Generalized Gibbs
Ensemble (GGE).
