  We consider an inflationary model based only on renormalizable superpotential
terms in which a superheavy scale F-term hybrid inflation (FHI) is followed by
a Peccei-Quinn (PQ) phase transition. We show that the field which triggers the
PQ phase transition influences drastically the inflationary dynamics and that
the Universe undergoes a secondary phase of reheating after the PQ phase
transition. Confronting FHI with the current observational data we find that,
for the central value of the spectral index, the grand unification scale can
assume its supersymmetric value for more or less natural values for the
remaining model parameters. On the other hand, the final reheat temperature
after the PQ phase transition turns out to be low enough to avoid the gravitino
problem.
