  We investigate the effect of electron-phonon inelastic scattering on shot
noise in nanoscale junctions in the regime of quasi-ballistic transport. We
predict that when the local temperature of the junction is larger than its
lowest vibrational mode energy $eV_c$, the inelastic contribution to shot noise
(conductance) increases (decreases) with bias as $V$ ($\sqrt{V}$). The
corresponding Fano factor thus increases as $\sqrt{V}$. We also show that the
inelastic contribution to the Fano factor saturates with increasing thermal
current exchanged between the junction and the bulk electrodes to a value
which, for $V>>V_c$, is independent of bias. A measurement of shot noise may
thus provide information about the local temperature and heat dissipation in
nanoscale conductors.
