An ice-making system is adapted to operate within a section of a refrigeration appliance where the ice-making system and the ice made in the ice-making system are exposed to a temperature greater than zero degrees Centigrade. When installed in the fresh food compartment of a refrigerator that also has a freezer section compartment, the refrigeration system furnishes a cooling effect to the freezer compartment sufficient to maintain the freezer compartment at a temperature of zero degrees or less and separately furnish to the ice-making unit a cooling effect sufficient to freeze water for making ice in the ice-making unit of the ice-making system. The ice-making system can include a reservoir that is operatively associated with the ice-making unit of the ice-making system for delivering water to the ice-making unit and for receiving water returned from the ice-making unit.