  We investigate the free energy and entropy of the Gaussian massive scalar
field theory in the static de Sitter space-time for arbitrary temperature. For
the inverse temperatures of the form $\beta=2 \pi 2^k, \ \ k\in \mathbf{Z}$, in
curvature units, we find the explicit form of the free energy and its
derivatives with respect to the temperature. There are two types of
contributions to the free energy: one is of the "area type" and can be
attributed to the horizon, while the other is of the "volume type" and is
associated with the interior of the space-time. The latter contribution in the
odd-dimensional case in the limit of the week field (large mass or small Hubble
constant) significantly depends on the temperature. Namely, for $ \beta<2\pi$,
the free energy behaves as $ F^{bulk}_{\beta} \sim e^{- \beta \, m} $, while
for $\beta>2\pi$ it behaves as $ F^{bulk}_{\beta} \sim e^{- 2 \, \pi \, m}$. We
also show that even the leading UV contributions to the free energy
significantly depend on the state of the theory, which is very unusual. We
explain the origin and physical meaning of these observations. As the model
example we consider the situation in the Rindler wedge of the flat space-time.
