  We consider nanowires in the field effect transistor device configuration.
Modeling each nanowire as a one dimensional lattice with random site
potentials, we study the heat exchanges between the nanowire electrons and the
substrate phonons, when electron transport is due to phonon-assisted hops
between localized states. Shifting the nanowire conduction band with a metallic
gate induces different behaviors. When the Fermi potential is located near the
band center, a bias voltage gives rise to small local heat exchanges which
fluctuate randomly along the nanowire. When it is located near one of the band
edges, the bias voltage yields heat currents which flow mainly from the
substrate towards the nanowire near one boundary of the nanowire, and in the
opposite direction near the other boundary. This opens interesting perspectives
for heat management at submicron scales: Arrays of parallel gated nanowires
could be used for a field control of phonon emission/absorption.
