  We present constraints on the reheating era within the string Fibre Inflation
scenario, in terms of the effective equation-of-state parameter of the
reheating fluid, $w_{reh}$. The results of the analysis, completely independent
on the details of the inflaton physics around the vacuum, illustrate the
behavior of the number of $e$-foldings during the reheating stage, $N_{reh}$,
and of the final reheating temperature, $T_{reh}$, as functions of the scalar
spectral index, $n_s$. We analyze our results with respect to the current
bounds given by the PLANCK mission data and to upcoming cosmological
experiments. We find that large values of the equation-of-state parameter
($w_{reh}>1/3$) are particularly favored as the scalar spectral index is of the
order of $n_s\sim 0.9680$, with a $\sigma_{n_s}\sim 0.002$ error. Moreover, we
compare the behavior of the general reheating functions $N_{reh}$ and $T_{reh}$
in the Fibre Inflation scenario with that extracted by the class of the
$\alpha$-attractor models with $\alpha=2$. We find that the corresponding
reheating curves are very similar in the two cases.
