  In this paper, we compute the mass and the temperature of the uncharged black
holes of third order Lovelock gravity and compute the entropy through the use
of first law of thermodynamics. We perform a stability analysis by studying the
curves of temperature versus the mass parameter, and find that there exists an
intermediate thermodynamically unstable phase for black holes with hyperbolic
horizon. The existence of this unstable phase for the uncharged topological
black holes of third order Lovelock gravity does not occur in the lower order
Lovelock gravity. We also perform a stability analysis for a spherical,
7-dimensional black hole of Lovelock gravity and find that while these kinds of
black holes for small values of Lovelock coefficients have an intermediate
unstable phase, they are stable for large values of Lovelock coefficients. We
also find that there exists an intermediate unstable phase for these black
holes in higher dimensions. This stability analysis shows that the
thermodynamic stability of black holes with curved horizons is not a robust
feature of all the generalized theories of gravity.
