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High-temperature properties of ceria surfaces are important for many applications. Here, we report the temperature dependencies of surface energy for (111) and (110) CeO₂ obtained in the framework of the extended two-stage up-sampled thermodynamic integration using Langevin dynamics. The method was used together with machine-learning potentials called moment tensor potentials (MTPs), which were fitted to the results of the ab initio molecular dynamics calculations for (111) and (110) CeO₂ at different temperatures. The parameters of MTP training and fitting were tested, and the optimal algorithm for the ceria systems was proposed. We found that the temperature increases from 0 to 2100 K led to the decrease of the Helmholtz free energy of (111) CeO₂ from 0.78 to 0.64 J/m². The energy of (110) CeO₂ dropped from 1.19 J/m² at 0 K to 0.92 J/m² at 1800 K. We show that it is important to consider anharmonicity, as simple consideration of volume expansion gives the wrong temperature dependencies of the surface energies.