  An exact linear response expression is obtained for the heat current in a
classical Hamiltonian system coupled to heat baths with time-dependent
temperatures. The expression is equally valid at zero and finite frequencies.
We present numerical results on the frequency dependence of the response
function for three different one-dimensional models of coupled oscillators
connected to Langevin baths with oscillating temperatures. For momentum
conserving systems, a low frequency peak is seen that, is higher than the zero
frequency response for large systems. For momentum non-conserving systems,
there is no low frequency peak. The momentum non-conserving system is expected
to satisfy Fourier's law, however, at the single bond level, we do not see any
clear agreement with the predictions of the diffusion equation even at low
frequencies. We also derive an exact analytical expression for the response of
a chain of harmonic oscillators to a (not necessarily small) temperature
difference; the agreement with the linear response simulation results for the
same system is excellent.
