By "thaw the line" do you mean the water fill? There should be no water coming in if the ice maker is off, or in between fill cycles. If water is freezing in the inlet, perhaps the valve is slowly leaking? Otherwise, there is sometimes a problem with water "sticking" to the plastic inlet tube. It freezes in small amounts and builds up a plug. This can be fixed by removing the tube, cleaning it, and applying a thin coat of food grade silicone grease.