Comments on the thermodynamics of little string theory

We study the high energy thermodynamics of little string theory, using its holographic description. This leads to the entropy-energy relation S = beta E-H + alpha log E + O(1/E). We compute alpha and show that it is negative; as a consequence, the high energy thermodynamics is unstable. We exhibit a mode localized near the horizon of the black brane, which has winding numb er one around euclidean time and a mass that vanishes at large E (or beta - -> beta (H)). We argue that the high temperature phase of the theory involv es condensation of this mode.