Phonon spectra as well as thermodynamic characteristics of superlattices are analyzed using the method of two-time, temperature dependent Green's functions. The phonon dispersion law is found in the "'cut-off" case. Free and internal energy of the system, as well as its specific heat and entropy are determined. The temperature behavior of the specific heat of a superlattice is compared to specific heats of bulk structures and those of thin films. It has been shown that, at extremely low temperatures, superlattice and film specific heats are practically equal and considerably lower than the specific heat of bulk sample. The consequences of this fact to thermal, conducting and superconducting properties of materials have been discussed.