The first thing I would check is to make sure the faucets on the external shower are both off. If they are open and the shower head is closed you can get a cross feed that can cause some strange symptoms.
Next I would let a little water out of the relief valve on the heater and see what the temp of The water in the heater is. On a standard 5 gallon it should be about 140 degrees. On one with a mixing valve it should be about 160 degrees. These are usually found on ten gallon units I think but may be on five gallon units.
If the temp is low I would check the winterizing dirverter valve for a small leak and the mixing valve if your system has one. In general you will want to look for a cross feed from cold to hot.
If the temp is low I would suspect the thermostat.