A method and device for producing a press-quenched part having a rim hole with a collar formed at the periphery of the rim hole includes inserting a temperature-controlled die into the rim hole of the part. The temperature of the temperature-controlled die is controlled such that the temperature of the part in a region of the collar is held above the martensite start temperature of the material from which the part is made. While the temperature of the collar is being held above the martensite start temperature, the remainder of the part is press quenched.