  The surface gravity for the extreme Reissner-Nordstr\"om black hole is zero
suggesting that it has a zero temperature. However, the direct evaluation of
the Bogolubov's coefficients, using the standard semi-classical analysis,
indicates that the temperature of the extreme black hole is ill definite: the
Bogolubov's coefficients obtained by performing the usual analysis of a
collapsing model of a thin shell, and employing the geometrical optical
approximation, do not obey the normalization conditions. We argue that the
failure of the employement of semi-classical analysis for the extreme black
hole is due to the absence of orthonormal quantum modes in the vicinity of the
event horizon in this particular case.
