The analytical model for the determination of contact temperature and wear on a working surface of friction brakes is presented. It is assumed that one of the friction element is composed of a periodic two-layered composite and the second element is a homogeneous half-space. In the frictional process, the wear coefficient is linearly dependent on the contact temperature. The influences of composite parameters as well as a parameter characterizing the changing of loading from zero to the nominal value on the distribution of contact temperature and wear during braking is considered.