Stationary observers in the space-time of a Schwarzschild black hole and accelerating observers in Minkowski space-time are both predicted to measure a particular temperature: the Hawking temperature for the fixed observer near a black hole, the Unruh temperature for the accelerated observer. We compare the temperatures and, for the same local acceleration, these observers are predicted to measure different temperatures. This allows one to distinguish the two cases locally and gives a violation of the equivalence principle. As the static observer nears the black hole approaches the horizon the two temperatures approach the same value and the equivalence principle is restored.