Phonon spectra and allowed phonon states, as well as thermodynamic characteristics of nanowires of simple cubic crystalline structure, are analyzed using the method of two-time dependent Green's functions, adjusted to bounded crystalline structures. Poles of Green's functions, defining phonon spectra, can be found by solving of the secular equation. For different boundary parameters, this problem is presented graphically. The presence of boundaries as well as the change of boundary parameters leads to appearance of new properties of low dimensional structures (thin film and nanowire). The most important feature is that beside allowed energy zones (which are continuous as in the bulk structure), zones of forbidden states appear. Different values of boundary parameters lead to appearance of lower and upper energy gaps, or dispersion branches spreading out of bulk energy zone. The correlation with spectra of phonons in corresponding unbounded structures is maintained in the work. Determination of phonon spectra and allowed phonon energies has great importance for kinetic and thermodynamic properties of semiconductive nanostructures and devices. The temperature behavior of nanowire thermal capacitance is compared to that of bulk structures. It is shown that at extremely low temperature nanowire thermal capacitance is considerably lower than the thermal capacitance of bulk sample. It was discussed what are the consequences of this fact to the thermal, conducting and superconducting properties of materials.