The paper presents a second order friction model for the joints of industrial robot manipulators that takes into account temperature effects. A solution based on a polynomial description of the friction is proposed. The theoretical analysis and the experimental measurements have shown that friction decreases with increasing temperature, which in turn depends on the working cycle of the manipulator. The mathematical model here proposed allows to foresee the friction variation during extensive working cycles and it does not require the use of a transducer for the measurement of the joint internal temperature; therefore it is well suitable for low-cost industrial applications, to improve the control performance or to predict the energy consumption. Experimental tests performed on a commercial 6 DOF manipulator show that the model is effective in estimating the joint temperature and the friction torque during the robot operations.