  We investigate the properties of a harmonic chain in contact with a thermal
bath at one end and subjected, at its other end, to a periodic force. The
particles also undergo a random velocity reversal action, which results in a
finite heat conductivity of the system. We prove the approach of the system to
a time periodic state and compute the heat current, equal to the time averaged
work done on the system, in that state. This work approaches a finite positive
value as the length of the chain increases. Rescaling space, the strength
and/or the period of the force leads to a macroscopic temperature profile
corresponding to the stationary solution of a continuum heat equation with
Dirichlet-Neumann boundary conditions.
