The empirical rate- and state-dependent friction law is widely used to explain the frictional resistance of rocks. However, the constitutive parameters vary with temperature and sliding velocity, preventing extrapolation of laboratory results to natural conditions. Here, we explain the frictional properties of natural gouge from the San Andreas Fault, Alpine Fault, and the Nankai Trough from room temperature to $\sim300^\circ$C for a wide range of slip-rates with constant constitutive parameters by invoking the competition between two healing mechanisms with different thermodynamic properties. A transition from velocity-strengthening to velocity-weakening at steady-state can be attained either by decreasing the slip-rate or by increasing temperature. Our study provides a framework to understand the physics underlying the slip-rate and state dependence of friction and the dependence of frictional properties on ambient physical conditions.