We study thermal leptogenesis in a broad class of supersymmetric SO(10) models with a leftright symmetric seesaw mechanism, taking into account flavour effects and the contribution of the next-to-lightest right-handed neutrino supermultiplet. Assuming M D = M u and a normal hierarchy of light neutrino masses, we show that four out of the eight right-handed neutrino mass spectra reconstructed from low-energy neutrino data can lead to successful leptogenesis with a reheating temperature in the (10 9 − 10 10 ) GeV range. In the remaining four solutions, leptogenesis is dominated by N 2 decays, as in the type I seesaw case. We find that some of these spectra can generate the observed baryon asymmetry for reheating temperatures above 10 10 GeV, in contrast to the type I case. Together with flavour effects, an accurate description of charged fermion masses turns out to be a crucial ingredient in the analysis.