A theoretical and experimental analysis of the heat conductivity in metal-dielectric point contacts is given. The contribution of the phonon diffraction effects to the heat conductivity is investigated. The phonon heat transport through the point contacts is measured from 0.1 K to 100 K using the anvil-needle technique. In KBr-KBr and KBr-Cu point contacts, substituting a Cu needle for the dielectric cold edge does not disturb the heat conductivity pattern. Measurements for Si-Cu point contacts reveal well-defined diffraction maxima of reduced heat conductivity at temperatures in the range 0.5 K-1 K.