A mixing and cooling system that performs mixing cycles for managing temperatures of rubber mixtures discharged from a mixer having a converging conical twin-screw mixer with a fixed frame that supports sleeves in which two screws are mounted at an angle between an opening arranged upstream of the sleeves, where an introduction hopper of the machine feeds the screws, and an outlet arranged downstream of the sleeves, where the mixer discharges the mixture at the end of a mixing process of the mixing cycle, one or more motors that rotate the two screws in the sleeves during the mixing process, and one or more movable doors provided at the outlet that allow, during the mixing process, the discharge and shaping of a rubber mixture, characterized in that the system comprises: a screw mixing and extrusion machine comprising: the mixer; a ram with an inner surface having a shape that is complementary to an outer contour of the two screws, the ram moving along the inside of an introduction hopper; a roller nose system comprising two counter-rotating rollers arranged just downstream of the outlet to form a sheet of the mixture discharged from the mixer; and one or more mobile sleeves that are arranged top-down towards the outlet, the mobile sleeves comprising mobile elements that move linearly with respect to the outlet so as to adjust a predetermined space between the sleeves and the screws; and a cooling system including: at least one spray installation comprising a spray station (102, 104) that delivers water at a predetermined water flow rate to a sheet exiting the machine; at least one suction installation proportionate to each spray installation that suctions air at a predetermined air flow rate; and at least one transport means (114, 116) that transports the sheet in a predetermined direction corresponding to a cooling process realized by the cooling system. a screw mixing and extrusion machine comprising: the mixer; a ram with an inner surface having a shape that is complementary to an outer contour of the two screws, the ram moving along the inside of an introduction hopper; a roller nose system comprising two counter-rotating rollers arranged just downstream of the outlet to form a sheet of the mixture discharged from the mixer; and one or more mobile sleeves that are arranged top-down towards the outlet, the mobile sleeves comprising mobile elements that move linearly with respect to the outlet so as to adjust a predetermined space between the sleeves and the screws; the mixer; a ram with an inner surface having a shape that is complementary to an outer contour of the two screws, the ram moving along the inside of an introduction hopper; a roller nose system comprising two counter-rotating rollers arranged just downstream of the outlet to form a sheet of the mixture discharged from the mixer; and one or more mobile sleeves that are arranged top-down towards the outlet, the mobile sleeves comprising mobile elements that move linearly with respect to the outlet so as to adjust a predetermined space between the sleeves and the screws; and a cooling system including: at least one spray installation comprising a spray station (102, 104) that delivers water at a predetermined water flow rate to a sheet exiting the machine; at least one suction installation proportionate to each spray installation that suctions air at a predetermined air flow rate; and at least one transport means (114, 116) that transports the sheet in a predetermined direction corresponding to a cooling process realized by the cooling system. at least one spray installation comprising a spray station (102, 104) that delivers water at a predetermined water flow rate to a sheet exiting the machine; at least one suction installation proportionate to each spray installation that suctions air at a predetermined air flow rate; and at least one transport means (114, 116) that transports the sheet in a predetermined direction corresponding to a cooling process realized by the cooling system.