  Reheating in string compactifications is generically driven by the decay of
the lightest modulus which produces Standard Model particles, dark matter and
light hidden sector degrees of freedom that behave as dark radiation. This
common origin allows us to find an interesting correlation between dark matter
and dark radiation. By combining present upper bounds on the effective number
of neutrino species N_eff with lower bounds on the reheating temperature as a
function of the dark matter mass m_DM from Fermi data, we obtain strong
constraints on the (N_eff,m_DM)-plane. Most of the allowed region in this plane
corresponds to non-thermal scenarios with Higgsino-like dark matter. Thermal
dark matter can be allowed only if N_eff tends to its Standard Model value. We
show that the above situation is realised in models with perturbative moduli
stabilisation where the production of dark radiation is unavoidable since bulk
closed string axions remain light and do not get eaten up by anomalous U(1)s.
