Recent theories predict that short-range quantum fluctuation forces (van der Waals and Casimir) and long-range electrostatic forces couple atomic vibrations across ˚Angstr¨om- to nanometer-scale vacuum gaps, opening a heat transfer channel termed phonon tunneling that coexists with near field radiative heat transfer. Resolving this phenomenon addresses fundamental questions about the partition of heat transfer modes at the atomic scale and establishes the ultimate heat flux limit across interfaces; yet experiments have yielded contradictory results. Here we use scanning thermal probes to quantify heat transfer between metallic surfaces at room temperature down to 3 ˚A, and benchmark the measurements against fluctuational electrodynamics and atomistic Green’s function calculations with realistically mapped three-dimensional probe geometry. Above 1 nm, we detect no electrostatic phonon tunneling. At sub-nm gaps, where contamination-mediated conduction cannot be excluded, the heat flux–distance power law deviates significantly from predictions for van der Waals- and Casimir-mediated phonon tunneling. These findings place noise-limited constraints on phonon tunneling above 1 nm and a conservative, contamination-inclusive upper bound at sub-nm separations in the conduction–radiation crossover regime.