We discuss numerical results from integrability for the Hagedorn temperature in N=4 SYM and ABJM theory at strong coupling and compare them to the Hagedorn temperatures of their string theory duals. From the numerics we conjecture the leading analytic coefficients in the expansion about large 't Hooft coupling. This talk is based on arXiv:2306.09883 and arXiv:2307.02350.