Electric and Hybrid-Electric Aircraft (HEA) propulsion system designs shall bring challenges at aircraft and systems level, mainly in propulsion, electric and thermal management systems (TMS). The electrification of the propulsion system relies on large and high-power electrical equipment (e.g., electrical motors, converters, power electronics, batteries, and others) that dissipate heat at a rate at least one order of magnitude higher than conventional propulsion aircraft systems. As a result, high impacts on weight, drag and power consumption of the TMS/cooling systems at the aircraft level are expected. This paper proposes potential technologies to perform the thermal management of future electric and HEA, in the context of FUTPRINT50 project. For each technology, relevant aspects such as its integration to aircraft, safety, operational and maintenance impacts, certification, technologies readiness level (TRL) and the latest research works are analysed. A quantitative comparison of the several technologies is also proposed considering weight, volume, electric power consumption, pneumatic air flow and cooling air flow per cooling effect. Lastly, we present a set of potential TMS architectures for HEA.