  We study qubit-mediated energy transfer between two electron reservoirs by
adopting a numerically-exact influence functional path-integral method. This
non-perturbative technique allows us to study the system's dynamics beyond the
weak coupling limit. Our simulations for the energy current indicate that
perturbative-Markovian Master equation predictions significantly deviate from
exact numerical results already at intermediate coupling, $\pi \rho
\alpha_{j,j'}\gtrsim 0.4$, where $\rho$ is the metal (Fermi sea) density of
states, taken as a constant, and $\alpha_{j,j'}$ is the scattering potential
energy of electrons, between the $j$ and $j'$ states. Markovian Master equation
techniques should be therefore used with caution beyond the strictly weak
subsystem-bath coupling limit, especially when a quantitative knowledge of
transport characteristics is desired.
