An approach based on considerations of the non-classical energy momentum tensor outside the event horizon of a black hole provides additional physical insight into the nature of discrete quantum hair on black holes and its effect on black hole temperature. Our analysis both extends previous work based on the Euclidean action techniques, and corrects an omission in that work. We also raise several issues related to the effects of instantons on black hole thermodynamics and the relation between these effects and results in two dimensional quantum field theory.

13 pages, Latex, submitted to Physical Review Letters