We study perturbative reheating at the end of fibre inflation where the inflaton is a closed string modulus with a Starobinsky-like potential .
We first derive the spectral index n _ { s } and the tensor-to-scalar ratio r as a function of the number of efoldings and the parameter R which controls slow-roll breaking corrections .
We then compute the inflaton couplings and decay rates into ultra-light bulk axions and visible sector fields on D7-branes wrapping the inflaton divisor .
This leads to a reheating temperature of order 10 ^ { 10 } GeV which requires 52 efoldings .
Ultra-light axions contribute to dark radiation even if \Delta N _ { eff } is almost negligible in the generic case where the visible sector D7-stack supports a non-zero gauge flux .
If the parameter R is chosen to be small enough , n _ { s } \simeq 0.965 is then in perfect agreement with current observations while r turns out to be of order r \simeq 0.007 .
If instead the flux on the inflaton divisor is turned off , \Delta N _ { eff } \lesssim 0.6 which , when used as a prior for Planck data , requires n _ { s } \simeq 0.99 .
After R is fixed to obtain such a value of n _ { s } , primordial gravity waves are larger since r \simeq 0.01 .