The thermal conductivities of thin crystalline semiconductor films in novel electrical and optical devices can differ from bulk values due to the size effect on lattice thermal conductivity, which is caused by phonon-boundary scattering. For many semiconductors at or above room temperature, the size effect is strongly influenced by the highly dispersive nature of their phonon spectra and the varying contribution of each phonon branch to heat conduction. The present study reviews existing thermal conductivity models for bulk semiconductor samples and examines the impact of the phonon dispersion on the size effect. Based on the observed strong dependence of the size effect on the phonon branch contributions, we demonstrate that the investigation of thin-film thermal conductivity at high temperatures can help the theoretical understanding of lattice thermal conduction. For silicon thin films studied here better agreement between the predicted in-plane thermal conductivity and the existing experimental data is achieved by assuming that longitudinal phonons are the dominant heat carriers. The practically-relevant problem of phonon scattering at the interface between crystalline silicon and amorphous silicon dioxide layers is discussed.