A cooling device for cooling a material to be cooled, comprising an inlet for a cooling medium conducted into a first, upper chamber of the cooling device. First conduits are provided which conduct the cooling medium from the upper chamber into a second, lower chamber of the cooling device. The upper chamber is separated from the lower chamber by a wall. Second conduits are provided which conduct the cooling medium from the lower chamber to at least one outlet opening for cooling medium, via which the cooling medium is discharged onto the material to be cooled.