Improved thermal management of power electronics is vital for improved device reliability and performance. Devices used for applications in next-generation mobile communications and internet of things, such as high-power high-frequency power amplifiers, and propulsion of electric vehicles and space missions, such as power switches, must handle high power dissipation with a large degree of Joule self-heating. To enable further development in these fields, improved thermal management is a necessity. Near channel, heterogeneously integrated heatsinks and spreaders are one aspect of the technology required to meet this challenge. In this thesis, the mechanical and thermal properties of the semiconductor-heatsink interface have been studied. This interface is key for determining the reliability of devices and accessing the heatsink's benefits. Various methods of integrating AlGaN/GaN high electron mobility transistors with diamond have been investigated. In addition, the thermal properties of Si-on-SiC have been studied, aiming to understand the thermal benefit of this material over silicon-on-insulator. An improved analysis method has been developed to investigate the mechanical stability of heterogeneously integrated thin films on stiff substrates, demonstrated in GaN-on-diamond. This method has increased reliability and accuracy compared to previous analyses. In addition to mechanical investigations, the thermal properties of novel GaN-on-diamond materials have been studied. The use of crystalline Al₀.₃₂Ga₀.₆₈N and SiC interlayers have been demonstrated, showing good promise for SiC layers with comparable effective thermal boundary resistance (TBReff) to state-of-the-art GaN-on-diamond using SiNₓ (30±5 m² K GW⁻¹). A multi-step diamond growth procedure has also been investigated and found to give record low TBReff of < 5 m² K GW⁻¹. Finally, thermal characterisation of the heterointerface was undertaken on direct-bonded Si-on-SiC. The interface of this material exhibited excellent thermal properties with TBReff < 10 m² K GW⁻¹. Simulations suggest this material could offer significant thermal improvements over conventional silicon-on-insulator for power converters.