  We use the global embedding Minkowski space (GEMS) geometries of a
(3+1)-dimensional curved Reissner-Nordstr\"om(RN)-AdS black hole spacetime into
a (5+2)-dimensional flat spacetime to define a proper local temperature, which
remains finite at the event horizon, for freely falling observers outside a
static black hole. Our extended results include the known limiting cases of the
RN, Schwarzschild--AdS, and Schwarzschild black holes.
