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This paper presents the results of calculating the Casimir–Lifshitz friction force and the heating rate of a small metal particle moving above a metal surface (thick plate) in the case of their different local temperatures. The case of normal nonmagnetic metals (Au) is considered. There is a strong interplay of temperatures, particle velocity, and separation distance, which leads to an anomalous direction of the heat flow between bodies and a peak temperature dependence of the friction force at sufficiently low temperatures of the order of 1–10 K. In particular, a “hot” moving particle can additionally receive heat from a “cold” surface. The conditions for experimental measurement of these effects are discussed.