A machine for making and dispensing cold or iced products includes: an element for containing the product to be dispensed and equipped with a mouth for dispensing the food product; a dispenser located at the mouth for dispensing the food product and able to be turned on or off to allow the food product to be dispensed; a thermal treatment cylinder; a stirrer, coaxial with the thermal treatment cylinder and adapted to rotate about a respective axis of rotation; a refrigeration system in which a refrigerant fluid circulates and includes an evaporator associated with the thermal treatment cylinder, a condenser, a pressure reducing element and a compressor; wherein the evaporator includes a first tubular member and a second tubular member extending along an axial direction parallel to the axis of rotation X, the second tubular member being inserted inside the first tubular member to define an annular chamber extending uninterruptedly.