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

Hard gluon evolution in warming medium