In a method for the internal cooling of a rotating object (4), liquid gas from at least one inlet channel (61) in a fixed object (5) is pressed into a ring-shaped groove (62) located between the fixed object (5) and the rotating object (4). From the ring-shaped groove (62) the liquid gas is pressed into at least one channel (63, 64.1, 64.2) in the rotating object (4) and brought to a part to be cooled (15). The liquid gas, upon contact with the part, evaporates and expands while absorbing heat, thereby cooling the part. The area surrounding the part to be cooled (15) may be designed as an expansion chamber (65). The method can be used to cool molded parts in injection molding machines with rotating molds (1), thereby achieving shorter cycle times.