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Your hot water demands must be very low! My family could never do that!
A modern high efficiency gas water heater, one that is condensing, brings the temperature of the exhuast gases below 100 C. Like most thermodynamic cycles, even a flame is more efficient at higher temperatures. These units have no pilot light, as they feature electronic ignition. When they're off, no natural gas is being consumed.
You can also put a insulating jacket on it.
There are get a reverse flow heat exhanger that goes in the drain pipe to warm the water going into the tank. This can save a lot of hot water from going down the drain.
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