We have developed a theoretical model to predict the thermal conductivity across the boundary between two solids. Our approach is based on solving Boltzmann equation taking into account all the physical aspects of the phonon scattering mechanisms. Distinction between normal processes which tend to displace the phonon distribution from its equilibrium one and resistive processes which restore it back is emphasized in our analysis. Lattice vibration parameters that enter in the thermal conductivity calculation, the Debye temperature and the Gruneissen paramter, are taken to be temperature dependent. At the boundary, we consider that transmission of phonons can be diffusive or specular, the probability of each depends on incident phonon characteristics such as its incidence angle and wavelength, as well as the interface roughness. With this theoretical model in hand, the thermal conductivity of polycrystalline materials can be calculated. As a second application of our new model, we employ it to predict materials that can be used in the form of nanostructured superlattices to obtain systems of extremely low thermal conductivity.