We systematically investigate constraints on the parameters of the supersymmetric type-I seesaw mechanism from the requirement of successful thermal leptogenesis in the presence of upper bounds on the reheat temperature T RH of the early Universe. To this end, we solve the flavour-dependent Boltzmann equations in the MSSM, extended to include reheating. With conservative bounds on T RH , leading to mildly constrained scenarios for thermal leptogenesis, compatibility with observation can be obtained for extensive new regions of the parameter space, due to flavour-dependent effects. On the other hand, the hypothesis that the right-handed neutrino sector conserves CP, and that leptogenesis exclusively arises from the CPviolating phases of the U MNS matrix, is only marginally consistent. Taking into account stricter bounds on T RH further suggests that (additional) sources of CP violation must arise from the right-handed neutrino sector, further implying stronger constraints for the right-handed neutrino parameters.