  Temperature effects in a scalar field non-minimally coupled to gravity are
investigated. The Thermo Field Dynamics formalism is used. This is a
topological field theory that allows us to calculate different effects, such as
the Stefan-Boltzmann law and the Casimir effect, on an equal footing. These
phenomena are calculated assuming the G\"odel space-time as a gravitational
background. A possible implication of these results at the beginning of the
universe is discussed.
