A cooled cryostat device comprising: a cold finger having infrared detector means secured to the end thereof; an outer casing surrounding the cold finger; and stiffener means for stiffening the cold finger and interposed between the outer casing and the cold finger in the vicinity of the end thereof. The stiffener means comprising: first eyelets provided on the inside of the casing and around its periphery; second eyelets provided on the outside of the cold finger around its periphery; the first and second eyelets being mutually angularly offset; and a cable tensioned around a closed loop between the outer casing and the cold finger and passing freely through the first and second eyelets, with the cable, once the cold finger has been placed in a balanced situation, itself being secured to the outer casing and to the cold finger.