This paper presents the design of a Fault Detection and Isolation scheme to improve the reliability of a cryogenic engine test bench operation, focusing specifically on its cooling circuit. The proposed fault detection consists in an extended unknown input observer, a cumulative sum algorithm and an exponentially moving average chart. A dynamic parity space approach is then proposed to isolate one or two simultaneous faults in the cooling circuit. The initial system model, for each line composing the cooling circuit, is augmented with constraints based on the mass flow rate continuity and the energy conservation for the overall system. Time delays in the transients are accounted for by recursive equations over a sliding window. The method allows settling adaptive thresholds that avoid pessimistic decision about the continuation of tests while detecting and isolating faults in the transient and permanent states of the system. The model structure and the estimation method were validated on the real Mascotte test bench (ONERA/CNES) data. The fault detection and isolation scheme was validated in realistic simulations.