  After inflation the Universe presumably undergoes a phase of reheating which
in effect starts the thermal big bang cosmology. However, so far we have very
little direct experimental or observational evidence of this important phase of
the Universe. In this letter, we argue that measuring the spectrum of freely
propagating relativistic particles, i.e. dark radiation, produced during
reheating may provide us with powerful information on the reheating phase. To
demonstrate this possibility we consider a situation where the dark radiation
is produced in the decays of heavy, non-relativistic particles. We show that
the spectrum crucially depends on whether the heavy particle once dominated the
Universe or not. Characteristic features caused by the dependence on the number
of the relativistic degrees of freedom may even allow to infer the temperature
when the decay of the heavy particle occurred.
