Strained transition layers, which are common for heteroepitaxial growth of functional semiconductors on foreign substrates, include high defect densities that impair heat conduction. Here, we measure the thermal resistances of AlN transition layers for GaN on Si and SiC substrates in the temperature range 300 < T < 550 K using time-domain thermoreflectance. We propose a model for the effective resistance of such transition films, which accounts for the coupled effects of phonon scattering on defects and the two interfaces. The data are consistent with this model using point defects at concentrations near 10(20) cm(-3) and transmission coefficients based on the diffuse mismatch model. The data can be also described using lower transmission coefficients and eliminating the defects in the AlN. The data and modeling support the hypothesis that point defect scattering in the AlN film dominates the resistance, but may also be consistent with a high presence of near-interfacial defects in the bounding films.