  Black holes arising in the context of scalar-tensor gravity theories, where
the scalar field is non-minimally coupled to the curvature term, have zero
surface gravity. Hence, it is generally stated that their Hawking temperature
is zero, irrespectivelly of their gravitational and scalar charges. The proper
analysis of the Hawking temperature requires to study the propagation of
quantum fields in the space-time determined by these objects. We study scalar
fields in the vicinity of the horizon of these black holes. It is shown that
the scalar modes do not form an orthonormal set. Hence, the Hilbert space is
ill-definite in this case, and no notion of temperature can be extracted for
such objects.
