  Building on the recently established connection between the Hagedorn
temperature and integrability [Phys.Rev.Lett. 120 (2018) no.7, 071605], we show
how the Quantum Spectral Curve formalism can be used to calculate the Hagedorn
temperature of AdS5/CFT4 for any value of the 't Hooft coupling. We solve this
finite system of finite-difference equations perturbatively at weak coupling
and numerically at finite coupling. We confirm previous results at weak
coupling and obtain the previously unknown three-loop Hagedorn temperature. Our
finite-coupling results interpolate between weak and strong coupling and allow
us to extract the first perturbative order at strong coupling. Our results
indicate that the Hagedorn temperature for large 't Hooft coupling approaches
that of type IIB string theory in ten-dimensional Minkowski space.
