  We consider the Hamiltonian dynamics and thermodynamics of spherically
symmetric spacetimes within a one-parameter family of five-dimensional Lovelock
theories. We adopt boundary conditions that make every classical solution part
of a black hole exterior, with the spacelike hypersurfaces extending from the
horizon bifurcation three-sphere to a timelike boundary with fixed intrinsic
metric. The constraints are simplified by a Kucha\v{r}-type canonical
transformation, and the theory is reduced to its true dynamical degrees of
freedom. After quantization, the trace of the analytically continued Lorentzian
time evolution operator is interpreted as the partition function of a
thermodynamical canonical ensemble. Whenever the partition function is
dominated by a Euclidean black hole solution, the entropy is given by the
Lovelock analogue of the Bekenstein-Hawking entropy; in particular, in the low
temperature limit the system exhibits a dominant classical solution that has no
counterpart in Einstein's theory. The asymptotically flat space limit of the
partition function does not exist. The results indicate qualitative robustness
of the thermodynamics of five-dimensional Einstein theory upon the addition of
a nontrivial Lovelock term.
