A machine for making and dispensing cold or ice beverages, such as cool drinks, slushes, sorbets and the like, comprising at least: - a containment and processing tank for the product to be dispensed which has a front wall, which is equipped at the bottom of it with a dispensing mouth for dispensing the beverage, - a dispenser, located at the beverage dispensing mouth and able to be turned on or off to allow the beverage to be dispensed; - a thermal treatment cylinder located inside the containment tank; - a stirrer located outside an outer surface of said thermal treatment cylinder and adapted to rotate about a respective axis of rotation; - a thermal treatment plant comprising a first cooling circuit and a second heating circuit, the first cooling circuit being defined at least by a first exchanger associated with the thermal treatment cylinder, by a second heat exchanger, by an auxiliary exchanger, by a pressure reducing unit, by a compressor and by respective pipes (36, 35), and the second circuit being defined at least by the first exchanger associated with the thermal treatment cylinder, by the auxiliary exchanger, by the compressor and by respective pipes (32, 30), the thermal treatment plant also comprising a selective connecting unit configured for turning on, in a first cooling configuration, the first cooling circuit, for applying a thermodynamic cooling cycle to the product in the tank, or for turning on, in a second heating configuration, the second heating circuit, for applying a hot gas thermodynamic heating cycle to the product in the tank, also comprising an electronic control and drive unit operatively connected to the selective connecting unit, for controlling it in such a way as to switch it to the two configurations, that is to say, between the first configuration and the second configuration and a selection interface, operatively acting on said electronic control and drive unit and comprising at least one control for setting the configuration of the selective connecting unit, between the first and the second operating configurations. - a containment and processing tank for the product to be dispensed which has a front wall, which is equipped at the bottom of it with a dispensing mouth for dispensing the beverage, - a dispenser, located at the beverage dispensing mouth and able to be turned on or off to allow the beverage to be dispensed; - a thermal treatment cylinder located inside the containment tank; - a stirrer located outside an outer surface of said thermal treatment cylinder and adapted to rotate about a respective axis of rotation; - a thermal treatment plant comprising a first cooling circuit and a second heating circuit, the first cooling circuit being defined at least by a first exchanger associated with the thermal treatment cylinder, by a second heat exchanger, by an auxiliary exchanger, by a pressure reducing unit, by a compressor and by respective pipes (36, 35), and the second circuit being defined at least by the first exchanger associated with the thermal treatment cylinder, by the auxiliary exchanger, by the compressor and by respective pipes (32, 30), the thermal treatment plant also comprising a selective connecting unit configured for turning on, in a first cooling configuration, the first cooling circuit, for applying a thermodynamic cooling cycle to the product in the tank, or for turning on, in a second heating configuration, the second heating circuit, for applying a hot gas thermodynamic heating cycle to the product in the tank, also comprising an electronic control and drive unit operatively connected to the selective connecting unit, for controlling it in such a way as to switch it to the two configurations, that is to say, between the first configuration and the second configuration and a selection interface, operatively acting on said electronic control and drive unit and comprising at least one control for setting the configuration of the selective connecting unit, between the first and the second operating configurations.