A machine for making liquid or semi-liquid products, including: a processing container for processing a basic liquid or semi-liquid product, defining a processing chamber and provided with a stirrer rotating inside the processing chamber; a thermal treatment system associated with the processing container for heating and/or cooling the processing chamber; a dispensing device which is associated with the processing container to receive therefrom the processed, basic liquid or semi-liquid product, and which is equipped with controls for delivering the processed, basic liquid or semi-liquid product to the outside of the processing container; an electronic control unit for controlling at least one actuator of the machine, a plurality of syrup containers, at least one heating and/or cooling device connectable to one or more of the syrup containers and/or connecting pipes and/or pumps in order to thermally treat the syrups.