A cooling apparatus (10) for cooling a detector (52), the cooling apparatus including an inner and an outer countercurrent heat exchanger (12 and 14, respectively) for a first and a second gas in a thermally insulating housing (16), the inner countercurrent heat exchanger (12) being arranged within a sublength of the outer countercurrent heat exchanger (14), and the inner countercurrent heat exchanger (12) being spatially separated from the outer countercurrent heat exchanger (14) by an outer sleeve (18). In this apparatus, the outer sleeve (18) has a partition plate (32) between an expansion nozzle (28) for the first gas located at the end of the inner countercurrent heat exchanger (12) and the remaining part of the outer countercurrent heat exchanger (14).