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We generalize the formalism proposed by Dalibard, Dupont-Roc, andCohen-Tannoudji [the DDC formalism] in the fourth order for two atoms ininteraction with scalar fields in vacuum to a thermal bath at finitetemperature $T$, and then calculate the interatomic interaction energy of twoground-state atoms separately in terms of the contributions of thermalfluctuations and the radiation reaction of the atoms and analyze in detail thethermal corrections to the van der Waals and Casimir-Polder interactions. Wediscover a particular region, i.e., $\sqrt[4]{\lambda^3\beta}\ll L\ll \lambda$with $L$, $\beta$ and $\lambda$ denoting the interatomic separation, thewavelength of thermal photons and the transition wavelength of the atomsrespectively, where the thermal corrections remarkably render the van der Waalsforce, which is usually attractive, repulsive, leading to an interestingcrossover phenomenon of the interatomic interaction from attractive torepulsive as the temperature increases. We also find that the thermalcorrections cause significant changes to the Casimir-Polder force when thetemperature is sufficiently high, resulting in an attractive force proportionalto $TL^{-3}$ in the $\lambda\ll\beta\ll L$ region, and a force which can beeither attractive or repulsive and even vanishing in the $ \beta\ll\lambda\llL$ region depending on the interatomic separation.

Quantum thermal field fluctuation induced corrections to the interaction between two ground-state atoms