  We study quantum fields on spacetimes having a bifurcate Killing horizon by
allowing the possibility that left- and right- (in-going and out-going) modes
have different temperatures. We consider in particular the Rindler for both
massless and massive fields, the static de Sitter and Schwarzschild black hole
backgrounds for massive fields. We find that in all three cases, when any of
the temperatures is different from the canonical one (Unruh, Hawking and
Gibbons--Hawking, correspondingly) the correlation functions have extra
singularities at the horizon.
