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

Finite temperature corrections to the energy-momentum tensor at one-loop in static space-times