Do I need to replace the thermostat or element in my hot water heater?

As old as that water heater is, you'll probably end up replacing it before it's all over. For all you know, it might be too old to obtain parts for easily. You might want to start getting plumbers' estimates now. The abnormally hot water is a sign that your thermostat is starting to fail. If you're lucky, eventually your water heater will simply fail to heat your water. If you're unlucky, it'll leak, really bad news if it lives in a closet with carpeting. If you can afford it, you might also think of getting a water system--hard water can reduce the efficiency of a water heater, as well as shortening the life of your fixtures.