You dont want them outside. Droopy can become a problem. Pics would be great actually..

Did you cut the leaves in half? You have to make sure its humid inside the dome since it doesnt have roots for water intake. You need to keep the rootzone warm for sure. I dont have a heating mat either but this is what I do. I set up my clone dome above my flowering tent ballast. It keeps it nice and warm. When the ballast is off I put a lamp under the clone dome and the bulb heat keeps it warm. Warm rootzone is important for proper and quick rooting.