I have never had a problem with outdoor temps as long as they are kept shaded and don't allow the sun to fall directly on the container which would heat it up way to much. There is always the possibility of some wilting depending on the type of plant, but the high humidity in the box help control that. Plants wilt because they loose moisture through there leaves. You can minimize this by removing all but the top couple of leaves and if the leaves that are left are large you can cut them in half. I'm not sure what the ideal temperature for cuttings is, but they need warmth to develop roots and I have had plenty of success with this method.
If I were going to try rooting indoors I would use the same method but I would leave the top off the container, place it in a bright window and add a soil heat mat under the container.
