Nanomaterials will play a disruptive role in next-generation thermal management for high power electronics in aerospace platforms. These high power and high frequency devices have been experiencing a paradigm shift toward designs that favor extreme integration and compaction. The reduction in form factor amplifies the intensity of the thermal loads and imposes extreme requirements on the thermal management architecture for reliable operation. In this perspective, we introduce the opportunities and challenges enabled by rationally integrating nanomaterials along the entire thermal resistance chain, beginning at the high heat flux source up to the system-level heat rejection. Using gallium nitride radio frequency devices as a case study, we employ a combination of viewpoints comprised of original research, academic literature, and industry adoption of emerging nanotechnologies being used to construct advanced thermal management architectures. We consider the benefits and challenges for nanomaterials along the entire thermal pathway from synthetic diamond and on-chip microfluidics at the heat source to vertically-aligned copper nanowires and nanoporous media along the heat rejection pathway. We then propose a vision for a materials-by-design approach to the rational engineering of complex nanostructures to achieve tunable property combinations on demand. These strategies offer a snapshot of the opportunities enabled by the rational design of nanomaterials to mitigate thermal constraints and approach the limits of performance in complex aerospace electronics.