We present constraints on the reheating era within the string Fiber 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 fiber Inflation scenario with the one 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 .