To optimize the thermal design of AlGaN-GaN high-electron-mobility transistors (HEMTs), which incorporate high power densities, an accurate prediction of the underlying thermal transport mechanisms is crucial. Here, a HEMT-structure (Al0.17Ga0.83N, GaN, Al0.32Ga0.68N and AlN on a Si substrate) was investigated using a time-domain thermoreflectance (TDTR) setup. The different scattering contributions were investigated in the framework of phonon transport models (Callaway, Holland and Born-von-Karman). The thermal conductivities of all layers were found to decrease with a temperature between 300 K and 773 K, due to Umklapp scattering. The measurement showed that the AlN and GaN thermal conductivities were a magnitude higher than the thermal conductivity of Al0.32Ga0.68N and Al0.17Ga0.83N due to defect scattering. The layer thicknesses of the HEMT structure are in the length scale of the phonon mean free path, causing a reduction of their intrinsic thermal conductivity. The size-effect of the cross-plane thermal conductivity was investigated, which showed that the phonon transport model is a critical factor. At 300 K, we obtained a thermal conductivity of (130 ± 38) Wm−1K−1 for the (167 ± 7) nm thick AlN, (220 ± 38) Wm−1K−1 for the (1065 ± 7) nm thick GaN, (11.2 ± 0.7) Wm−1K−1 for the (423 ± 5) nm thick Al0.32Ga0.68N, and (9.7 ± 0.6) Wm−1K−1 for the (65 ± 5) nm thick Al0.17Ga0.83N. Respectively, these conductivity values were found to be 24%, 90%, 28% and 16% of the bulk values, using the Born-von-Karman model together with the Hua–Minnich suppression function approach. The thermal interface conductance as extracted from the TDTR measurements was compared to results given by the diffuse mismatch model and the phonon radiation limit, suggesting contributions from inelastic phonon-scattering processes at the interface. The knowledge of the individual thermal transport mechanisms is essential for understanding the thermal characteristics of the HEMT, and it is useful for improving the thermal management of HEMTs and their reliability.