Molecular dynamics simulations, performed with chemically accurate ab initio machine-learning force fields, are used to demonstrate that layer stiffness has profound effects on the superlubricant state of two-dimensional van der Waals heterostructures. We engineer bilayers of different rigidity but identical interlayer sliding energy surface and show that a 2-fold increase in the intralayer stiffness reduces the friction by a factor of ∼6. Two sliding regimes as a function of the sliding velocity are found. At a low velocity, the heat generated by the motion is efficiently exchanged between the layers and the friction is independent of the layer order. In contrast, at a high velocity, the friction heat flux cannot be exchanged fast enough and a buildup of significant temperature gradients between the layers is observed. In this situation, the temperature profile depends on whether the slider is softer than the substrate.