The decisive experimental evidence of enhanced heat conduction driven by surface phonon polaritons (SPhPs) has been recently demonstrated along polar nanofilms. However, a proper quantitative interpretation remains to be fully established. In this work, we provide a consistent theoretical explanation of the measured thermal conductivities of polar nanofilms, based on a coupled Boltzmann transport equation and heat diffusion equation for describing the dynamics of SPhPs and phonons, respectively. This formalism enables to separately quantify the SPhP and phonon contributions to the in-plane heat transport and shows the overestimation of the SPhP thermal conductivity predicted by previous empirical model for predominant boundary scattering. This study, thus, promotes the understanding of the observed thermal conductivity enhancement driven by SPhPs, as a novel heat conduction channel for heat dissipation applications in nanoelectronics and optoelectronics.