  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 $\Delta N_{\rm eff}$ 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,
$\Delta N_{\rm eff}\lesssim 0.6$ 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 $r\simeq 0.01$.
