  We study the thermalization dynamics of an impurity cloud inside a
Bose-Einstein condensate at finite temperature, introducing a suitable
Boltzmann equation. Some values of the temperature and of the initial impurity
energy are considered. We find that, below the Landau critical velocity, the
macroscopic population of the initial impurity state reduces its depletion
rate. For sufficiently high velocities the opposite effect occurs. For
appropriate parameters the collisions cool the condensate. The maximum cooling
per impurity atom is obtained with multiple collisions.
