The part I'm wondering about is the decision to lower the temperature while out, meaning that when you get back the furnace is going to have to run for a longer time to heat a house back up to a comfortable level that it does to maintain a temperature*.
It's the same answer, really!
If in cold weather, you keep the house at a higher temperature, it will lose heat more quickly, requiring lots more energy to compensate for the heat loss.
If you allow the temperature to drop overnight, or while out for a few hours, then this will slow down the loss of heat, saving energy. When you later turn the thermostat back up, sure the furnace will run longer than "usual" to raise the overall temperature. But there's simply no way that this can cost more energy than it would by keeping the house at a high temperature all of the time.
It's not about _temperature_. It's about heat (energy) loss. The less energy you lose, the less it takes to replace that energy. Turning the thermostat down for a few hours reduces heat loss.
Cheers