New equations for heat capacities, entropies, and enthalpies were applied to the experimental constant volume heat capacity data of diamond. The temperature Theta(V) corresponding to 3R=2 was found to be 468 K. The relationships between dimension, and Theta(V) and the Debye temperature were given. Diamond showed the dimensionality crossover from 3 to 2 at after 300 K. Temperature dependences of the Debye temperature and Theta(V) were given and non-monotonic behaviors were discussed. The heat capacity and entropy values predicted by the proposed models were compared with the values predicted by the Debye models. The results showed that the proposed models fit the data better than the Debye models. The enthalpy values predicted by the proposed models were compared with the values predicted by the polynomial model and good agreement was obtained.