Manipulating interfacial thermal transport is important for many technologies including nanoelectronics, solid-state lighting, energy generation and nanocomposites(1-3). Here, we demonstrate the use of a strongly bonding organic nanomolecular monolayer (NML) at model metal/dielectric interfaces to obtain up to a fourfold increase in the interfacial thermal conductance, to values as high as 430 MW m(-2) K-1 in the copper-silica system. We also show that the approach of using an NML can be implemented to tune the interfacial thermal conductance in other materials systems. Molecular dynamics simulations indicate that the remarkable enhancement we observe is due to strong NML-dielectric and NML-metal bonds that facilitate efficient heat transfer through the NML. Our results underscore the importance of interfacial bond strength as a means to describe and control interfacial thermal transport in a variety of materials systems.