A cooling device is disclosed for a radiation detector including a detector surface and a plurality of collimator plates arranged in the direction of X-radiation before the detector surface. In order to produce the cooling device of at least one embodiment, the collimator plates are designed and/or the cooling device includes a ventilation device which is designed, so that the space between the collimator plates is at least partially exposed to a cooling air flow in order to cool the radiation detector. A corresponding method for cooling an X-radiation detector is furthermore described in at least one additional embodiment.