Systems and methods using container holders configured to provide a stable support for containers held therein in order to efficiently cool the containers after a hot-fill or elevated temperature operation. The container holders can allow a fluid to pass from an inner volume of the container holder to outside the container holder through side apertures and/or an open bottom end of the container holder. Groups of containers and container holders also may be cooled. Groups of containers in container holders can be processed through the cooling operation at a speed different from a speed for holderless containers.