  We discuss the energy current and the energy fluctuations in an isolated
quantum wire driven far from equilibrium. The system consists of interacting
spinless fermions and is driven by a time--dependent magnetic flux. The energy
current is defined by the continuity equation for the energy density which is
derived both for homogeneous as well as for inhomogeneous systems. Since the
total energy is not conserved in the driven system, the continuity equation
includes the source terms which are shown to represent the Joule heating
effects. For short times and weak drivings the energy current agrees with the
linear response theory. For stronger fields or longer times of driving the
system enters the quasiequilibrium regime when the energy current gradually
diminishes due to the heating effects. Finally, for even stronger driving the
energy current is shown to undergo a damped Bloch oscillations. The energy
spread also increases upon driving. However, the time--dependence of this
quantity in the low field regime is quite unexpected since it is determined
mostly by the time of driving being quite independent of the instantaneous
energy of the system.
