  The one-loop quantum corrections to the free energy associated with scalar
field in a higher dimensional static curved space-time is investigated making
use of the conformal transformation method. For a space-time with bifurcate
horizon, horizon divergences are accounted for choosing the Planck length as
natural cutoff. The leading term in the high temperature quantum correction
satifies holographically the "area law", like the tree level Bekenstein-Hawking
term. Furthermore it is stressed that only for the asymptotically AdS black
holes one may have a microscopic interpretation of the entropy also at quantum
level.
