The invention relates to a system for manufacturing polymer parts, comprising: a material-injection portion, a mould movable between at least one open position and a closed position, the mould comprising an outer mould portion, wherein the injection portion is suitable for injecting material into the closed mould so as to form at least one part when the injection portion is connected to the closed mould, and wherein the system is suitable for moving the injection portion relative to the mould after injection, the outer portion being kept in contact with the part formed by injection in order to cool the part during the movement of the injection portion.