  Within the framework of the "brick wall model", a novel method is developed
to compute the contributions of a scalar field to the thermodynamic quantities
of black holes. The relations between (transverse) momenta and frequencies in
Rindler space are determined numerically with high accuracy and analytically
with an accuracy of better than 10 % and are compared with the corresponding
quantities in Minkowski space. In conflict with earlier results, the
thermodynamic properties of black holes turn out to be those of a low
temperature system. The resulting discrepancy for partition function and
entropy by two orders of magnitude is analyzed in detail. In the final part we
carry out the analogous studies for scalar fields in de Sitter space and
thereby confirm that our method applies also to the important case of
spherically symmetric spaces.
