Is a capacitor bad when it looks like this?
Since this a heat related problem, as everyone has stated it is probably an electrolytic capacitor which is more than likely true. The best way to test for the heat related capacitors is with a can of circuit cooler. Canned Air Dusters will work very well if turned upside down. Allow equipment to warm up and volume has gone down. Then spray some capacitors in one area of the board, allow a few seconds for the coolant to take effect. If you have hit the right one the volume will return. If not select another area to cool four or five capacitors.
When finding the right area allow it to warm up again, then selectively spray one at a time each capacitor, allowing time for it to take effect. When you hit the right one, replace it. Some cases may have several capacitors bad.