We explore a model of heat transport between two heat reservoirs mediated by a quantum particle. The reservoirs are modeled as ensembles of harmonic modes linearly coupled to the mediator. The steady state heat current, as well as the thermal conductance are obtained for arbitrary coupling strength and will be analyzed for the cases of weak and strong coupling regimes. It is shown that the violation of the virial theorem – the imbalance between the average potential and kinetic energy of the mediator – can be considered as a measure of the coupling strength that takes into account all the relevant factors. The dependence of the thermal conductance on the coupling strength is non-monotonic and displays a maximum. Temperature dependence of the heat conductance may reach a plateau at intermediate temperatures, similar to the classical plateau at high temperatures. We will discuss the origin of Fourier’s law in a chain of macroscopically large, but finite subsystems coupled by the quantum mediators. We will also address the origin of the anomalously large heat current between the scanning tunneling microscope tip and the substrate in deep vacuum which was found in recent experiments.