  In large volume models reheating is driven by the decays of the volume
modulus to the visible sector, while the decays to its axion partners result in
dark radiation. In this article we discuss the impact of loop corrections on
the only model-independent visible decay channel: the decay into Higgs pairs
via a Giudice-Masiero term. Including such radiative effects leads to a more
precise determination of the relative fraction of dark radiation, since by
contrast all loop corrections to the volume axion decay mode are Planck
suppressed. Assuming an MSSM spectrum and that the Giudice-Masiero coupling is
fixed at the string scale by a shift symmetry in the Higgs sector, we arrive at
a prediction for the effective number of neutrinos. The result turns out to be
too large to be consistent with data, highly disfavouring the minimal model.
