  We study the high energy thermodynamics of Little String Theory, using its
holographic description. This leads to the entropy-energy relation $S=\beta_H
E+\alpha\log E+O(1/E)$. 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 number one
around Euclidean time and a mass that vanishes at large $E$ (or
$\beta\to\beta_H$). We argue that the high temperature phase of the theory
involves condensation of this mode.
