This thesis investigates the implementation of a cryocooler for the THESEUS (Transient High Energy Sky and Early Universe Surveyor) mission, one of the three candidate missions for the European Space Agency's (ESA) seventh medium-class scientific mission (M7), currently in its preliminary study phase (Phase A) since September 2023. The primary objective of THESEUS is to study gamma-ray bursts to enhance our understanding of the early evolution of the universe. Additionally, the mission includes monitoring X-ray transients and conducting infrared observations in response to external signals detected by dedicated sensors. To meet the stringent thermal requirements of the infrared observation sensor, the implementation of a cryogenic cooling system, either active or passive, is essential.