The interaction potential at finite temperature between two atoms in the asymptotic limit of large separations $R\gg\hbar c/k_{B}T$ is shown to be $V\left(R\right) = -3k_{B}T\alpha^{2}\left(0\right)/R^{6}$, identical to the expression for two classical polarizable dipoles. This is in contrast to the zero-temperature, large-separation Casimir-Polder retarded potential $V\left(R\right) = -23\hbar c\alpha^{2}\left(0\right)/4\pi R^{7}$. The result is demonstrated by taking the low-density limit in the Lifshitz theory of interacting macroscopic bodies, and independently through a quantum-electrodynamical fourth-order perturbation theory calculation with averaging over a thermally excited blackbody radiation field. An interpretation is offered in terms of the nature of the thermal excitations of the field, leading to a manifestation of the correspondence principle at sufficiently large interatomic distances.