A cooling and conveying apparatus (10) under vacuum, at a controlled temperature, has an inlet coupled with the outlet of the expansion chamber (4), and an outlet having an associated second gas-tight valve device (18) for discharging the expanded and cooled confectionery products (3). This apparatus (10) includes at least one cooling and conveying unit (11-14) comprising a conduit under vacuum (11a-14a) in which there is provided a worm conveyor device (11d-14d 11e-14e) including a flexible spiral screw (11e-14e) intended to cause a displacement of the expanded pieces (3) at a controlled speed.