We report measurements of the solid‐solid thermal boundary resistanceRbd, spanning the temperature range from 1 to 300 K. Below 30 K,Rbdis found to be in agreement with the prediction of the acoustic mismatch model. The influence of diffuse scattering at the interface is found to have a very minor influence onRbd. Above 30 K,Rbddecreases less rapidly with increasing temperature than predicted by the theory. Phonon scattering in thin (∼30 A˚) disordered layers near the interface is shown to be a possible explanation. Implications for heat removal from integrated circuits are discussed.