system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How does turning down the temperature while away from home actually save energy?

It seems to me that maintaining an internal temperature would require less energy than letting the house cool and then having to crank the furnace on high for an hour or more to raise the temperature back up to a comfortable level, assuming the external temperature is much colder than the internal temperature. 

Follow up question: When the external temperature is much colder than the internal temperature, are there any energy savings in keeping the internal temperature lower, say around 17 Celsius vs 21 Celsius?
gpt
> It seems to me that maintaining an internal temperature would require less energy than letting the house cool and then having to crank the furnace on high for an hour or more to raise the temperature back up to a comfortable level, assuming the external temperature is much colder than the internal temperature.  

Everything I've learned about heat transfer says this isn't true.  

In short, heat transfers faster when the temperature difference is greater.  

Heaters and A/C output a constant temperature when they're on, no matter what your thermostat is set to.  

Think of it this way, if it's 40 F outside and your thermostat us set to 70 F, you're trying to keep the house at a constant temperature. As soon as it hits 70 F, your heat shuts off, because 70 F to 40 F is a big difference, it loses heat very quickly. As the difference in temperature falls, the rate of heat loss also lowers. In comparison if you have your thermostat set to 60 or 65 while you're away, there is still a big difference from 60-65 down to 40 but that difference is less than from 70 down to 40, which means your house loses heat more slowly because your thermostat is lower. This means the heat doesn't run as often as if you try to keep it 70 the whole time.  

So yes, it may seem maintaining a higher temperature would be better, but the actual energy required to raise the house (in winter) from a maintained 65 F to 70 F when you return, is less than the energy required to maintain 70 F the entire time. This is because the greater the temperature difference between inside and outside your house, the more often your units have to turn on, the more often they turn on, the more energy they use. While on, they use the same energy whether they are heating the house 1 degree or 10 degrees, the only difference is how long they run, and heating the house 10 degrees takes less time than heating the house 1 degree 10 times (due to how heat transfer works).