Hot water temp fluctuation normal?

[Nelsonch]

I have my water heater set between "LOW" and the next highest setting on the gas thermostat, and it stays around 120 deg Far. but occassionally when I take the water temp at a nearby faucet it is as high as 124 deg. Is that kind of temp. fluctuation within normal range? Also just curious - can the heat generated by the pilot light flame be enough heat over time to slightly raise the water temp in the tank?

 

[RonAKA]

A natural gas water heater controls temperature by turning off and on. It does not modulate the burner firing rate. As a result of this it will be constantly cycling and the temperature will not be exactly constant. 4 deg F is a very minor temperature error and I would expect to be quite normal. The pilot light does not have a large amount of heat in it, and the large majority will be lost up the exhaust vent. It will not be enough to keep up with constant losses of heat through the insulation of the heater.