Controlled heat transfer and thermal rectification in a system of two coupled cavities connected to thermal reservoirs are discussed. Embedding a dispersively interacting two-level atom in one of the cavities allows switching from a thermally conducting to resisting behavior. By properly tuning the atomic state and system–reservoir parameters—in particular, system–reservoir couplings and resonance frequencies—the direction of the current can be reversed. It is shown that a large thermal rectification is achievable in this system by tuning the cavity–reservoir and cavity–atom couplings. Partial recovery of diffusive heat transport in an array of N cavities containing one dispersively coupled atom is discussed.