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Heat dissipation plays a crucial role in the performance and reliability of high-power GaN-based electronics. While AlN transition layers are commonly employed in the heteroepitaxial growth of GaN-on-SiC substrates, concerns have been raised about their impact on thermal transport across GaN/SiC interfaces. In this study, we present experimental measurements of the thermal boundary conductance (TBC) across GaN/SiC interfaces with varying thicknesses of the AlN transition layer (ranging from 0 to 73 nm) at different temperatures. Our findings reveal that the addition of an AlN transition layer leads to a notable increase in the TBC of the GaN/SiC interface, particularly at elevated temperatures. Structural characterization techniques are employed to understand the influence of the AlN transition layer on the crystalline quality of the GaN layer and its potential effects on interfacial thermal transport. To gain further insights into the trend of TBC, we conduct molecular dynamics simulations using high-fidelity deep learning-based interatomic potentials, which reproduce the experimentally observed enhancement in TBC even for atomically perfect interfaces. These results suggest that the enhanced TBC facilitated by the AlN intermediate layer could result from a combination of improved crystalline quality at the interface and the "phonon bridge" effect provided by AlN that enhances the overlap between the vibrational spectra of GaN and SiC.