Thermodynamics of TT, JT, TJ deformed conformal field theories

We compute the Hagedorn temperature of mu TT + epsilon +JT + epsilon -TJ deformed CFT using the universal kernel formula for the thermal partition function. We find a closed analytic expression for the free energy and the Hagedorn temperature as a function of mu, epsilon (+), and epsilon (-) for the case of a compact scalar boson by taking the large volume limit. We also compute the Hagedorn temperature for the single trace deformed AdS(3)x S(1)x T(3)x S-3 using holographic methods. We identify black hole configurations whose thermodynamics matches the functional dependence on (mu, epsilon (+), epsilon (-)) of the double trace deformed compact scalars.