Nanoscale solid-solid contacts are key elements which determine the electrical and thermal behavior of modern electronic devices and micro- and nanoelectromechanical systems. Here we show that simultaneous measurements of the shear force and the heat flow in nanoscale junctions reveal a linear correlation between thermal conductance and maximal shear force, confirming the ballistic nature of heat transport in the junction. Furthermore, we find that here the shear strength and thermal conductance in nanoscale contacts for materials where heat transport is phonon dominated can be linked via the fundamental material properties of heat capacity and group velocity of the heat carriers.