[en] We study the high energy thermodynamics of Little String Theory, using its holographic description. This leads to the entropy-energy relation S=β_HE+αlogE+O(1/E). We compute α 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 number one around Euclidean time and a mass that vanishes at large E (or β→β_H). We argue that the high temperature phase of the theory involves condensation of this mode. (author)