Turn it off.
Same misconception about letting your car idle vs. shutting it off, that it would use more fuel to crank then to idle for a short duration. Any furnace will use much less fuel to heat the house back up than it would use to keep the house continually warm throughout your absence. Think about it. The heat goes _somewhere_ and the warmer the house, the more heat there is to escape it. Outside. So keeping the furnace on just pumps heat outside. So turn it off.
Caveat: we’re assuming here that you’re not going away long enough to let the house temperature drop below freezing – frozen pipes = $$expensive. But setting the thermostat so that no place in your house gets below maybe a few degrees above should be fine.
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