  The high energy thermodynamics of Little String Theory (LST) is known to be
unstable. An unresolved question is whether the corresponding instability in
LST holographic dual is of stringy or supergravity origin. We study UV
thermodynamics of a large metric deformation of the LST dual realized (in the
extremal case) by type IIB fivebranes wrapping a two-sphere of a resolved
conifold, and demonstrate that the resulting black hole has negative specific
heat. This explicitly shows that the high energy thermodynamic instability of
the LST holographic dual is of the supergravity origin.
