We consider finite size effects on energy transfer between nanoparticles mediated by quantum systems. The nanoparticles are considered as heat reservoirs with a finite number of modes. An expression for the quasi-static energy transport between the heat reservoirs having a finite mode frequency spacing Δ is derived. The resulting equations describing long-term (t ≥1/Δ) relaxation for the mode temperatures and the average temperatures of the nanoparticles are solved. The solutions depend on small number of measurable parameters and show unusual peculiarities in their temporal variations. As is shown, Fourier’s law in a chain of identical subsystems (nanoparticles) can be validated only on a short time scale. For a larger times, when t ∼ 1/Δ, the temperatures of different modes deviate from each other, thus preventing thermal equilibrium in each subsystem, and the validity of Fourier’s law cannot be established.