A machine for dispensing blended iced beverages is characterized by a cabinet for storing a plurality of supplies of beverage ingredients and a refrigeration system for chilling an interior of the cabinet to chill the beverage ingredient supplies. A duct extends between the cabinet interior and a remote point of delivery of the beverage ingredients and a tubing bundle extends from the supplies and through the duct to the delivery point to deliver beverage ingredients from the supplies to the delivery point. The interior of the duct is chilled to chill the tubing bundle and beverage ingredients in the tubing bundle, so that chilled beverage ingredients are always provided to the point of delivery, even when the machine is idle for an extended period of time. Various techniques are provided for chilling the interior of the duct.