We establish a framework for calculating the Hagedorn temperature of
AdS5/CFT4 via integrability. Concretely, we derive the thermodynamic Bethe
ansatz equations that yield the Hagedorn temperature of planar N=4 super
Yang-Mills theory at any value of the 't Hooft coupling. We solve these
equations perturbatively at weak coupling via the associated Y-system,
confirming the known results at tree-level and one-loop order as well as
deriving the previously unknown two-loop Hagedorn temperature. Finally, we
comment on solving the equations at finite coupling.Comment: 6 pages; v3: references and further clarification added, matches
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