The alternator is not keeping up. From the moment that light stays on you are running on the battery alone, which in most cars is under an hour with the lights and fan going, and less at night.
Get it here while it still moves, or call us. It is usually brushes and a regulator, which is a rebuild; a burnt rotor means a new unit. We check the belt and the tensioner at the same time, since a glazed belt slipping on the pulley reads exactly the same on the dashboard.