  Formulating the statistical mechanics for a scalar field with non-minimal
$\xi R \phi^2$ coupling in a black hole background we propose modification of
the original 't Hooft ``brick wall'' prescription. Instead of the Dirichlet
condition we suggest some scattering ansatz for the field functions at the
horizon. This modifies the energy spectrum of the system and allows one to
obtain the statistical entropy dependent on the non-minimal coupling. For
$\xi<0$ the entropy renormalizes the classical Bekenstein-Hawking entropy in
the correct way and agrees with the result previously obtained within the
conical singularity approach. For a positive $\xi$, however, the results
differ.
