We have investigated the influence of thin films of a dielectric material on the near-field mediated heat transfer at the fundamental limit of single monolayer islands on a metallic substrate. We present spatially resolved measurements by near-field scanning thermal microscopy showing a distinct enhancement in heat transfer above NaCl islands compared to the bare Au(111) film. Experiments at this subnanometer scale call for a microscopic theory beyond the macroscopic fluctuational electrodynamics used to describe near-field heat transfer today. The method facilitates the possibility of developing designs of nanostructured surfaces with respect to specific requirements in heat transfer down to a single atomic layer.