Resonant tunneling of surface polaritons across a subwavelength vacuum gap between two polar or metallic bodies at different temperatures leads to an almost monochromatic heat transfer which can exceed by several orders of magnitude the far-field upper limit predicted by Planck’s blackbody theory. However, despite its strong magnitude, this transfer is very far from the maximum theoretical limit predicted in the near field. Here we propose an amplifier for the photon heat tunneling based on a passive relay system intercalated between the two bodies, which is able to partially compensate the intrinsic exponential damping of energy transmission probability thanks to three-body interaction mechanisms. As an immediate corollary, we show that the exalted transfer observed in the near field between two media can be exported at larger separation distances using such a relay. Photon heat tunneling assisted by three-body interactions enables novel applications for thermal management at nanoscale, near-field energy conversion and infrared spectroscopy.