I can assume that water heater is gas fired?? If that is the case then your problem lies with the thermostat calibration device.
What is happening is simply that the water is being heated up fine but the differential temperature between cut in and cut out (normally approx 10 – 15 degrees C)is greater that it should be and is allowing the water temperature to drop below the 15 degree C allowance before it tells the burner to fire up again to reheat.
This problem is normally only exeperienced first thing in the morning as during the day small amounts of hot water are drawn off and eventually activate the thermostat sensor to relight the burner – but overnight when there is no draw off the temp drops way below the min setting before it is activated when you run hot water first thing in the morning.
The only postive cure for this problem is to have a new thermostat fitted and calibrated by a suitably qualified gasfitter.
Selgas Services Ltd
Craftsman Gasfitters, Plumbers, Electrical Service Technicians