  Metallic atomic junctions pose the ultimate limit to the scaling of
electrical contacts. They serve as model systems to probe electrical and
thermal transport down to the atomic level as well as quantum effects occurring
in one-dimensional systems. Charge transport in atomic junctions has been
studied intensively in the last two decades. However, heat transport remains
poorly characterized because of significant experimental challenges.
Specifically the combination of high sensitivity to small heat fluxes and the
formation of stable atomic contacts has been a major hurdle for the development
of this field. Here we report on the realization of heat transfer measurements
through atomic junctions and analyze the thermal conductance of single atomic
gold contacts at room temperature. Simultaneous measurements of charge and heat
transport reveal the proportionality of electrical and thermal conductance,
quantized with the respective conductance quanta. This constitutes an atomic
scale verification of the well-known Wiedemann-Franz law. We anticipate that
our findings will be a major advance in enabling the investigation of heat
transport properties in molecular junctions, with meaningful implications
towards the manipulation of heat at the nanoscale
