We report on the behavior of cold Rb atoms trapped in an anharmonic gravitomagnetic potential. Remarkably, the position of the effective potential minimum is dependent on the initial temperature of the atomic ensemble. This effect is a consequence of the thermal nature of the sample and the anharmonicity of the combined potential. Besides a theoretical description, we carried out numerical simulations of the evolution of trapped clouds under different boundary conditions in terms of temperature and release position. Both theory and simulation are in good agreement with the experimental measurements obtained on cold atomic samples of 87 Rb prepared at different temperatures. Possible applications of the observed behavior can be a novel technique to measure the temperature of a trapped atomic cloud, and a way to spatially separate thermal and condensed phases in BEC experiments.