The mathematical model of non-stationary frictional heating in a pad-disc brake system is proposed. The problem of friction heat during braking with a constant deceleration has been formulated. The thermal resistance on a contact surface and convective cooling on a free surface of a pad have been both taken into account. The exact (in quadratures) solution of this problem has been obtained. In the case of constant specific power of friction (sliding with constant speed) the asymptotic solutions for small and large values of the time have been produced. They are simple engineer formulas suitable for obtaining a quick evaluation of the thermal regime of braking system. The numerical analysis has been executed for the chosen friction couples at sliding with either constant speed or with constant deceleration. (C) 2014 Elsevier Ltd. All rights reserved.