nd the Boltzmann transport equation. It is shown that: (1) a small difference between the permittivities of the substrate and superstrate of the film can generate giant propagation lengths and therefore remarkably enhances its thermal conductivity with respect to values obtained for a freestanding one. (2) The propagation of surface phonon-polaritons is present in a broad band of frequencies and exhibits its largest propagation lengths at the frequency where the absorption of energy is minimal. (3) The increase of the thermal conductivity of the film as its thickness decreases is higher when it is deposited on potassium bromide instead of being suspended in air. The difference in the thermal conductivity for these two systems increases with increasing temperature and reducing the film thickness. A thermal conductivity as high as 2.5 W/m K is obtained for a 30 nm-thick thin film at room temperature, which is about 1.8 times larger than its bulk phonon value. The obtained results show that the propagation of surface phonon-polaritons has the potential not only to offset the reduction of the phonon thermal conductivity of a nano thin film, when its sizes are scaled down, but also to enhance it, by choosing properly the permittivity of its substrate.