Spectra of possible phonon states, as well as thermodynamic characteristics of nanocrystals (ultrathin fllm and quantum wire) of simple cubic crystalline structure are analyzed in this paper, using the method of two-time dependent Green functions. From energy spectra and internal energy of the system the thermal capacitance of these structures in low temperature region is found. The temperature behavior of speciflc heat is compared to that of corresponding bulk structure. It is shown that at extremely low temperatures thermal capacitance of quantum wire is considerably lower than the thermal capacitance of fllm as well as the bulk sample. Consequences of this fact are discussed in detail and its in∞uence to thermodynamic properties of materials is estimated.