  We study thermal leptogenesis in a broad class of supersymmetric SO(10)
models with a left-right 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.
