  We study heat transport in a chain of harmonic oscillators with random
elastic collisions between nearest-neighbours. The equations of motion of the
covariance matrix are numerically solved for free and fixed boundary
conditions. In the thermodynamic limit, the shape of the temperature profile
and the value of the stationary heat flux depend on the choice of boundary
conditions. For free boundary conditions, they also depend on the coupling
strength with the heat baths. Moreover, we find a strong violation of local
equilibrium at the chain edges that determine two boundary layers of size
$\sqrt{N}$ (where $N$ is the chain length), that are characterized by a
different scaling behaviour from the bulk. Finally, we investigate the
relaxation towards the stationary state, finding two long time scales: the
first corresponds to the relaxation of the hydrodynamic modes; the second is a
manifestation of the finiteness of the system.
