We study qubit-mediated energy transfer between two electron reservoirs by adopting a numerically exact influence functional path-integral method. This nonperturbative technique allows us to study the system's dynamics beyond the weak coupling limit. Our simulations for the energy current indicate that perturbativeMarkovian master equation predictions significantly deviate from exact numerical results already at intermediate coupling πρα j,j 0.4, where ρ is the metal (Fermi sea) density of states, taken as a constant, and α j,j is the scattering potential energy of electrons, between the j and j states. Perturbative 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.