The thermal management system architectures proposed for hydrogen-powered propulsion technologies are critically reviewed and assessed. The objectives of this paper are to determine the system-level shortcomings and to recognise the remaining challenges and research questions that need to be sorted out in order to enable this disruptive technology to be utilised by propulsion system manufacturers. Initially, a scientometrics based co-word analysis is conducted to identify the milestones for the literature review as well as to illustrate the connections between relevant ideas by considering the patterns of co-occurrence of words. Then, a historical review of the proposed embodiments and concepts dating back to 1995 is followed. Next, feasible thermal management system architectures are classified into three distinct classes and its components are discussed. These architectures are further extended and adapted for the application of hydrogen-powered fuel cells in aviation. This climaxes with the assessment of the available evidence to verify the reasons why no hydrogen-powered propulsion thermal management system architecture has yet been approved for commercial production. Finally, the remaining research challenges are identified through a systematic examination of the critical areas in thermal management systems for application to hydrogen-powered air vehicles’ engine cooling. The proposed solutions are discussed from weight, cost, complexity, and impact points of view by a system-level assessment of the critical areas in the field.