A beverage making machine may be arranged to cool a precursor liquid in a tank using a cooling liquid in a cooling container disposed around the tank. The cooling liquid may be freezable to form ice, e.g., to provide the system with improved cooling capacity and/or speed. A plurality of fins may extend between the tank and the cooling container, with each of the plurality of fins being physically attached to the cooling container or the tank and being arranged to conduct heat from the tank and/or from the cooling liquid. The plurality of fins may include first portions attached to the tank and extending outwardly, and second portions attached to the cooling container and extending inwardly. Side surfaces of corresponding first and second portions may be in contact with each other to aid in transferring heat via the fin portions.