Friction-induced instabilities can be caused by different separate mechanisms such as elastodynamic or thermoelastic. This paper suggests another type of instability due to the temperature dependency of the coefficient of friction. The perturbations imposed on the surface temperature field during the frictional sliding can grow or decay. A stability criterion is formulated and a case study of a brake disk is performed with a simple model without including effects of transforming layer and chemical/physical properties change with temperature. The disk is rigid and the coefficient of friction depends on temperature. We show that the mechanism of instability can contribute to poor reproducibility of aircraft disk brake tests reported in the literature. We propose a method to increase the reproducibility by dividing the disk into several sectors with decreased thermal conductivity between the sectors.