Kapitza in 1941 discovered that heat flowing across a solid in contact with superfluid helium (<2 K) encounters a strong thermal resistance at the interface. Khalatnikov demonstrated theoretically that this constitutes a general phenomenon related to all interfaces at all temperatures, given the dependence of heat transmission on the acoustic impedance (sound velocity  ×  density) of each medium. For the solid/superfluid interface, the measured transmission of heat is almost one hundred times stronger than the Khalatnikov prediction. This discrepancy could be intuitively attributed to diffuse scattering of phonons at the interface but, despite several attempts a detailed quantitative comparison between theoretical and experimental findings to explain the occurrence of scattering and its contribution to heat transmission had been lacking. Here we show that when the thermal wavelength λ of phonons of the less dense medium (liquid 4He) becomes comparable to the r.m.s. surface roughness σ, the heat flux crossing the interface is amplified; in particular when σ ≈ 0.33λ, a spatial resonant mechanism occurs, as proposed by Adamenko and Fuks. We used a silicon single crystal whose surface roughness was controlled and characterized. The thermal boundary resistance measurements were performed from 0.4 to 2 K at different superfluid pressures ranging from saturated vapour pressure (SVP) to above 4He solidification, to eliminate all hypothetical artefact mechanisms. Our results demonstrate the physical conditions necessary for resonant phonon scattering to occur at all interfaces, and therefore constitute a benchmark in the design of nanoscale devices for heat monitoring.