Use an extension cord to ensure that you are able to use the blow dryer evenly in front of your windows.
Be sure to use kerosene in an open, well-ventilated area.
For stubborn scratches, use an abrasive polish approved for acrylic surfaces.
Sand acrylic just as you would a piece of wood. Hand, disc or belt sanders should all work fine, just be sure to keep the sander moving at all times to prevent damage.