  The finite-temperature one-loop effective potential for a scalar field in the
static de Sitter space-time is obtained. Within this framework, by using
zeta-function regularization, one can get, in the conformally invariant case,
the explicit expression for the stress tensor anomaly. Its value turns out to
depend on the thermal state of the system. This conclusion is different from
the one derived by other authors, who considered thermal properties of
ultraviolet divergences in static spaces ignoring the effects of horizons. The
behaviour of the effective potential in the ground state and in de
Sitter-invariant state is also studied, showing the role played by the
curvature on the minima.
