Abstract The utilization of hybrid electric propulsion concept in aviation offers a viable solution to address the limitations posed by the relatively low energy density of batteries in fully electric aviation. These hybrid systems enable the aircraft to achieve a significant range while simultaneously minimizing carbon emissions. While the individual components of a Hybrid Electric Propulsion (HEP) system, such as electric motors and batteries, are designed with high efficiency, their integration presents a significant challenge in the realm of thermal management. Designing an efficient system for managing the substantial waste heat generated by heat sources and effectively transferring it to heat sinks during various flight phases is a complex task. This challenge becomes even more critical as the design must adhere to system weight limits and prioritize aviation safety considerations. In this review article, we performed a systematic review of the challenges related to the key elements in a thermal management system. These elements encompass every component or subsystem that contributes to the thermal management of a generic hybrid-electric propulsion system. This includes electric motors and generators, batteries, heat exchangers, power transmission systems, power distribution systems, storages, fuel cells, cooling fluids and pipes, control system, pumps and fans. Following the identification of the challenges, the paper provides a comprehensive summary of the existing solutions that have been offered and pursued by the community to address the challenges. Furthermore, the paper also discusses emerging technologies related to each element, highlighting their potential in overcoming these challenges.