  For every Hilbert bimodule over a C*-algebra, there are natural gauge actions
of the circle on the associated Toeplitz algebra and Cuntz-Pimsner algebra, and
hence natural dynamics obtained by lifting these gauge actions to actions of
the real line. We study the KMS states of these dynamics for a family of
bimodules associated to local homeomorphisms on compact spaces. For inverse
temperatures larger than a certain critical value, we find a large simplex of
KMS states on the Toeplitz algebra, and we show that all KMS states on the
Cuntz-Pimsner algebra have inverse temperature at most this critical value. We
illustrate our results by considering the backward shift on the one-sided path
space of a finite graph, where we can use recent results about KMS states on
graph algebras to see what happens below the critical value. Our results about
KMS states on the Cuntz-Pimsner algebra of the shift show that recent
constraints on the range of inverse temperatures obtained by Thomsen are sharp.
