  In this manuscript, we present a temperature dependent Boltzmann equation for
the particles transport through a environmental reservoir, where the
temperature refers to the equilibrium temperature of reservoir, a new damping
force and a inverse damping relaxation time are derived based on the classical
Boltzmann equation, which have obvious influence on the external force and the
relaxation time of transport particles. For comparison, we also define a
non-equilibrium temperature for the transport particle by its distribution
function out of equilibrium, which is different from the equilibrium
temperature of reservoir. There exist heat transfer between the transport
particle and the reservoir, because the whole transport particles are in
non-equilibrium state. Finally, we illustrate them by an example of
one-dimensional transport procedure, the damping force and the non-equilibrium
temperature defined by us are shown numerically.

Statistical Mechanics;Quantum Physics