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This paper presents how the temperature dependence of the friction phenomena can be handled in mechanical control systems using state estimation techniques. The method is based on the dynamic friction model, originally introduced by Batista and Carlson (Physical Rev. E; 1996, 1998), where the temperature dependence of friction is described by an un-measurable internal state. According to the author's knowledge this model was not applied before in mechanical control system analysis and design. For the model a state estimator was developed based on the theory of hybrid systems. A robust tracking control algorithm was also developed for mechanical systems with temperature dependent friction. Simulation measurements are provided in the second part of the paper to show the applicability of the theoretical results.