The Casimir–Lifshitz friction force and the heating rates of two metal plates with a narrow vacuum gap between them during nonrelativistic motion of one of them are calculated analytically and numerically within the framework of fluctuation electrodynamics. Changes in material properties are taken into account using the Bloch-Grüneisen and modified Bloch-Grüneisen (with finite residual resistance) resistivity models within the Drude approximation. It is shown that identical plates with the same initial temperature have the same heating rate, determined by the power of the friction force, and the possibility of measuring the friction force from the heating kinetics of nonmagnetic metal plates with temperatures of 1–10 K is substantiated.