Axions that couple to electromagnetism are produced in the early Universe by, among other channels, freeze-in via the Primakoff process. For sufficiently large axion masses, the same coupling causes the axions to decay into two photons, which subsequently ionize the intergalactic medium. If this decay occurs in the redshift range $20\lesssim z\lesssim 1100$, then the contribution to the cosmic microwave background optical depth $\tau_{\rm reio}$ can lead to a conflict with observations, excluding models with sufficiently strongly coupled, heavy axions and high reheating temperatures, $T_{\rm reh}$. Using large ensembles of explicit type IIB string theory models with up to $h^{1,1}=100$ axions, we compute the full cosmic reionization history caused by the decays of multiple axions. We compare this to the posterior on the high-$z$ component of $\tau_{\rm reio}$ derived from parametric-independent constraints on the ionization state of the Universe, obtained in a full analysis presented in a companion paper. For $h^{1,1}=20,50,100$, we find that approximately 15%, 15%, and 10% of the models in the ensemble prefer $T_{\rm reh} \lesssim 10^{10}\,\text{GeV}$ at 95% CL. We provide a publicly available code at:~, which computes the reionization history for arbitrary ensembles of decaying axions. Our analysis opens the door for future large-scale work studying the preference for low-temperature reheating in models with multiple axions.