  We describe the energy distribution of hard gluons travelling through a dense
quark-gluon plasma whose temperature increases linearly with time, within a
probabilistic perturbative approach. The results were applied to the
thermalization problem in heavy ion collisions, in the third stage of the
bottom-up picture, to estimate the initial time for the third stage of the
bottom-up scenario. We then look at the entropy density and average temperature
of the soft thermal bath, as the system approaches (local) thermal equilibrium.
