We live i te country and have a well. When showering, the water starts off cool, which I understand as it has to go through the pipes from the hot water tank. Once it is hot, we turn the shower down to a comfortable lever but after about two or three minutes, the water is hot again. What could be happening? Doesn't the hot water come from the top of the tank and the cold replacement goes to the bottom?
It could be a heater problem, but if the pipes pipes are in a cool location, it could take some time for them to heat up. Water temp heat should be set no higher than 120 deg. If it continues to get too hot, reset the thermostat on the heater, and check its' operation.
You are correct in your description of how a water heater works. We usually get complaints the other way around........running out of water too soon.