The thermal management of highly irradiated silicon detectors may soon require cooling temperatures beyond the limits of -45°C for the currently applied technologies with CO2. The working fluid shall be able to approach ultra-low temperatures for large heat loads using small piping and withstand a significant amount of radiation. Among the short-listed candidates, the noble gas krypton appears as an interesting alternative for the future cooling infrastructure of particle trackers at CERN. In this work, the use of Krypton is investigated. Its favorable thermodynamic properties are analyzed with respect to the very harsh operational requirements present inside high energy particle detectors. A preliminary design of a low-temperature refrigeration cycle is proposed, and different transient scenarios commonly encountered during real-life detector operation are evaluated.