  We present two analytic applications of the fact that a hyperbolic group can
be endowed with a strongly hyperbolic metric. The first application concerns
the crossed-product C*-algebra defined by the action of a hyperbolic group on
its boundary. We construct a natural time flow, involving the Busemann cocycle
on the boundary. This flow has a natural KMS state, coming from the Hausdorff
measure on the boundary, which is furthermore unique when the group is
torsion-free. The second application is a short new proof of the fact that a
hyperbolic group admits a proper isometric action on an $\ell^p$-space, for
large enough $p$.
