Abstract: We investigate the non-equilibrium dynamics of a
chain of harmonic oscillators in contact with two stochastic
Langevin heat baths at different temperatures and undergoing
random collisions between neighbours that exchange their
momenta with a constant rate $\gamma$. By means of an
appropriate continuum limit, we solve the equations for the
covariance matrix to leading order in the stationary state,
and derive exact expressions for the temperature profile and
for the leading contribution of the energy current, which
scales as $1/\sqrt{\gamma N}$.  At finite times, we solve
adiabatically the equation describing the time evolution of
the temperature profile $T(y,t)$, obtaining that in the bulk
of the system, $T(y)$ evolves according to the energy
continuity equation, but with a space-time scaling that is
described by a fractional diffusion equation.