  The Hessling improvement of the Haag, Narnhofer and Stein principle is
analysed in the case of a massless scalar field propagating outside of an
extremal R-N black hole. It is found that this sort of ``Quantum (Einstein's)
Equivalence Principle'' selects only the R-N vacuum as a physically sensible
state, i.e., it selects the temperature $T=0$ only.
