The invention relates to a method for cooling and comminuting hot cement clinker (1) in a cooler (3) and a corresponding device, wherein the cooler (3) has an inlet area (5), a recuperation area (7), an end cooling area (17), at least one opening (10) for blowing cooling air (11) into the recuperation zone (7), a tertiary air line (13) for discharging heated cooling air (11), a discharge area ...