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It is shown that the dissipation of energy in an electron gas confined in a quantum well made of non-centrosymmetric crystal leads to a direct electric current. The current originates from the real-space shift of the wave packets of Bloch electrons at the electron scattering by phonons, which tends to restore thermal equilibrium between the electron and phonon subsystems. We develop a microscopic theory of such a phonogalvanic effect for narrow band gap zinc-blende quantum wells.