My sister recently called me for some insight on a discussion she was having with her roommates on how they could save money on their heating bills in their house in WY. She was trying to convince them that when they left the house, they needed to lower the thermostat from 64° F (which is already a pretty good setting) to 60°; basically, to follow my advice here.
Her roommates' contention was that by lowering the thermostat when they are away, the heating system will use more energy to get back up to 64 when they turn it back on. Therefore, they just want to leave the system at 64 all the time.
Unfortunately, this is a common misconception. In order to clear things up completely, I am going to take a direct quote from the government (EERE) and we all know they are never wrong:
A common misconception associated with thermostats is that a furnace works harder than normal to warm the space back to a comfortable temperature after the thermostat has been set back, resulting in little or no savings. This misconception has been dispelled by years of research and numerous studies. The fuel required to reheat a building to a comfortable temperature is roughly equal to the fuel saved as the building drops to the lower temperature. You save fuel between the time that the temperature stabilizes at the lower level and the next time heat is needed. So, the longer your house remains at the lower temperature, the more energy you save.
Still don't believe me? Think of it this way: Instead of being gone just a few hours, you decide you are tired of the cold and go to Hawaii for the rest of the winter. Do you honestly think you would be saving more energy by leaving your thermostat at 64º as opposed to lowering it (or turning it off) for the the amount of time you are sipping Mai Tai's and getting sun burned on the beach? I'm just re-iterating the above statement: "... the longer your house remains at the lower temperature, the more energy you save." It doesn't matter if this time period is a few hours, days, or years!
These facts don't change depending on if you live in a moderate, hot, or extremely cold climate. As long as your location follows the Laws of Thermodynamics (which unless you are in some other Universe, it does) this applies to you!
Happy Energy Saving!