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Accurate structural feature characterization of cyclic peptides (CPs), especially those with less than 10 residues and cis-peptide bonds, is challenging but important for the rational design of bioactive peptides. In this study, we performed high-temperature molecular dynamics (high-T MD) simulations on 250 CPs with random sequences and applied the point-adaptive k-nearest neighbors (PAk) method to estimate the free energies of millions of sampled conformations. Using this data set, we trained a SchNet-based deep learning model, termed CPconf_score, to predict the conformational free energies of CPs. We tested CPconf_score to identify near-native conformations from MD-sampled conformations of 50 CPs from the Cambridge Structural Database. Our method achieved accurate predictions for 41 out of 50 CPs with a backbone RMSD of less than 1.0 Å compared to crystal structures. In comparison, other advanced CP structure prediction tools, such as HighFold and Rosetta, successfully predicted 12 and 19 CPs, respectively.