The invention relates to machine for preparing frozen confectionery comprising receiving means (1) forming a seat for accommodating an essentially cup-shaped container (8), said receiving means comprising an heat exchange element (1a) having a heat exchange contact surface arranged to be in contact with an heat exchange portion (12) of the container (8) when the container is placed in the machine； wherein said heat exchange element(1a) has an inverted conical or curved shape or a plurality of inverted conical sections, or a combination of curved and inverted conical sections. The confectionery produced can be a frozen product such as soft ice or a chilled dessert such as mousse or whipped yogurt.
