  We study backaction effects of phonon heating due to tunneling electrons on
the current noise in atomic-sized junctions. Deriving a generalized kinetic
approximation within the extended Keldysh Green's functions technique, we
demonstrate the existence of a characteristic backaction contribution to the
noise in case of low external phonon damping. We provide a physically intuitive
interpretation of this contribution at large voltage in terms of slow
fluctuations of the phonon occupation, and show that it generally gives a
significant correction to the noise above the phonon emission threshold.
