Beverage-dispensing appliance having a chilled carbonator

A beverage-dispensing appliance comprising:

• a carbonation tank defining a tank volume, a water inlet upstream from the tank volume, a carbon dioxide inlet upstream from the tank volume, and a carbonated water outlet downstream from the tank volume;
• a carbonator jacket defining a jacket volume disposed about the carbonation tank, a jacket inlet upstream from the jacket volume, and a jacket outlet downstream from the jacket volume, the jacket inlet being disposed above the jacket outlet;
• a cold water line extending to the carbonator jacket in upstream fluid communication with the jacket inlet to direct a cold water flow to the tank volume;
• an ice bin spaced apart from the carbonation tank, the ice bin defining a drain aperture upstream from the cold water line to direct melt water thereto;
• and
• a pump in downstream fluid communication with the jacket outlet to selectively motivate water from the tank volume.