  We investigate the evolution of a particle in a Lorentz gas where the
background scatters move and collide with each other. As in the standard
Lorentz gas, we assume that the particle is negligibly light in comparison with
scatters. We show that the average particle speed grows in time as
t^{lambda/(4+lambda)} in three dimensions when the particle-scatter potential
diverges as r^{-lambda} in the small separation limit. The typical displacement
of the particle exhibits a universal linear growth in time independently on the
density of the background gas and the particle-scatter interaction. The
velocity and position distributions approach universal scaling forms. We
determine the former, while for the position distribution we establish
conjecturally exact scaling forms for the one and two-dimensional Lorentz gas.
