  By using ab-initio-accurate force fields and molecular dynamics simulations
we demonstrate that the layer stiffness has profound effects on the
superlubricant state of two-dimensional van der Waals heterostructures. These
are engineered to have identical inter-layer sliding energy surfaces, but
layers of different rigidity, so that the effects of the stiffness on the
microscopic friction in the superlubricant state can be isolated. A twofold
increase in the intra-layer stiffness reduces the friction by approximately a
factor six. Most importantly, we find two sliding regimes as a function of the
sliding velocity. At low velocity the heat generated by the motion is
efficiently exchanged between the layers and the friction is independent on
whether the sliding layer is softer or harder than the substrate. In contrast,
at high velocity the friction heat flux cannot be exchanged fast enough, and
the build up 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.
