The present invention provides a beverage machine with at least three distinct zones 1, 3, 4. A first zone 1 for storing a liquid or semi-liquid product at ambient temperature, a second zone 3 for processing the stored product, in particular for cooling the product to a predetermined serving temperature, and a third zone 4 for storing the cooled product and maintaining it at the predetermined serving temperature. From the third zone 4 an iced beverage can be dispensed.