The invention relates to a machine for preparing a cooled food product, comprising: a receiving seat (1), for accommodating an essentially cup-shaped container, comprising a heat exchange element (1a) having a heat exchange contact surface (21) arranged to be in contact with an outer surface of a side wall (8d) of the container when the container is placed in the machine, and a stirring unit (5) connectable to a stirring member (9) and arranged for driving the stirring member (9) according to a combination of movements, wherein at least one of the combination of movements has a component directed towards the interior of the container when placed in the receiving seat (1). The method further relates to a system comprising the machine and a container and a method of preparation.
