By setting it lower, you are making the house lose less heat to the outdoors - thus saving on gas during the day.
Heat transfer is proportional to the difference in the temperature. So you lose more heat from your house being at 20 and outside is -10 than when it is at 16 and -10 outside.
I suspect that is also more efficient for the furnace to go from 16 to 20 when you come home in a single shot than it is for it to go 18 to 20 continously throughout the day.
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