  We consider finite size effects on heat transfer between thermal reservoirs
mediated by a quantum system, where the number of modes in each reservoir is
finite. Our approach is based on the generalized quantum Langevin equation and
the thermal reservoirs are described as ensembles of oscillators within the
Drude-Ullersma model. A general expression for the heat current between the
thermal reservoirs in the long-time quasi-static regime, when an observation
time is of the order of $\Delta ^{-1}$ and $\Delta$ is the mode spacing
constant of a thermal reservoir, is obtained. The resulting equations that
govern the long-time relaxation for the mode temperatures and the average
temperatures of the reservoirs are derived and approximate analytical solutions
are found.
