  We investigate the possibility of statistical explanation of the black hole
entropy by counting quasi-bounded modes of thermal fluctuation in two
dimensional black hole spacetime. The black hole concerned is quantum in the
sense that it is in thermal equilibrium with its Hawking radiation. It is shown
that the fluctuation around such a black hole obeys a wave equation with a
potential whose peaks are located near the black hole and which is caused by
quantum effect. We can construct models in which the potential in the above
sense has several positive peaks and there are quai-bounded modes confined
between these peaks. This suggests that these modes contribute to the black
hole entropy. However it is shown that the entropy associated with these modes
dose not obey the ordinary area law. Therefore we can call these modes as an
additional thermal hair of the quantum black hole.
