  Finite temperature corrections to the effective potential and the
energy-momentum tensor of a scalar field are computed in a perturbed Minkoswki
space-time. We consider the explicit mode decomposition of the field in the
perturbed geometry and obtain analytical expressions in the non-relativistic
and ultra-relativistic limits to first order in scalar metric perturbations. In
the static case, our results are in agreement with previous calculations based
on the Schwinger-De Witt expansion which indicate that thermal effects in a
curved space-time can be encoded in the local Tolman temperature at leading
order in perturbations and in the adiabatic expansion. We also study the shift
of the effective potential minima produced by thermal corrections in the
presence of static gravitational fields. Finally we discuss the dependence on
the initial conditions set for the mode solutions.
