  In the No-Boundary Universe a primordial black hole is created from a
constrained gravitational instanton. The black hole created is immersed in the
de Sitter background with a positive cosmological constant. The constrained
instanton is characterized not only by the external parameters, the mass
parameter, charge and angular momentum, but also by one more internal
parameter, the identification period in the imaginary time coordinate. Although
the period has no effect on the black hole background, its inverse is the
temperature of the no-boundary state of the perturbation modes perceived by an
observer. By using the Bogoliubov transformation, we show that the perturbation
modes of both scalar and spinor fields are in thermal q equilibrium with the
black hole background at the arbitrary temperature. However, for the two
extreme cases, the de Sitter and the Nariai models, the no-boundary state
remains pure.
