A cooking apparatus includes a dual-chamber container with an inner container for holding a food item to be cooked and an outer container for maintaining contact between a temperature-controlled heat transfer liquid and the inner container while the food is being cooked. The dual-chamber container includes an inlet fluid port and outflow fluid port which may be coupled directly to corresponding fluid port connectors on a temperature control unit, or an intervening fluid coupling assembly may convey heat transfer liquid between the control unit and the dual-chamber container. Some control units are adapted to simultaneously control cooking temperature for more than one dual-chamber container. Some dual-chamber containers have a flexible inner container that is separable from an outer container which may be a rigid container or a flexible container.