Current methods to describe the thermodynamic behavior of many-particle systems are often based on perturbation theory with an unperturbed system consisting of free particles. Therefore, only a few methods are able to describe both strongly and weakly correlated systems along the same lines. In this article we propose a cumulant approach which allows for the evaluation of excitation energies and is especially appropriate to account for the thermodynamics at low temperatures. The method is an extension of a cumulant formalism which was recently proposed to study statical and dynamical properties of many-body systems at zero temperature. The present approach merges into the former one for vanishing temperature. As an application we investigate the thermodynamics of the hole-doped antiferromagnetic phase in high-temperature superconductors in the framework of the anisotropic (Formula presented)-(Formula presented) model.