This one is very simple: Turn down the thermostat at night!

We find it surprising that so many people (physicists included) find this a problem, so let's try to explain it in as straightforward a way as possible.

Here is the key idea. When you're "heating a house", all you are really doing, in the long run, is replacing the energy that is being lost to the outside through the walls. So the simplest way of finding out how much energy you have to supply is to find out how much energy is being lost through the walls. And the rate at which energy is lost to the outside depends, of course, on the walls. How big is the house? What are the walls made of? How thick are the walls? Are there open windows? And so on. Those are not our concern here. The rate at which energy is lost also depends on the temperature difference between indoors and outdoors, and the outdoor temperature is not something we can change. The thing you can control is the indoor temperature, with your hand on the thermostat. Lowering the indoor temperature means a smaller temperature difference between indooors and outdoors, and thus less energy lost to the outside, which in turn means less energy that you have to replace. That's all there is to it.

It's true that the heating system has to work extra hard to warm up the house in the morning, but that's balanced by the fact that in the first hours after you turn the thermostat down, you don't have to put energy in at all. And all night long, while the house is at 60, say, instead of 70, you're losing less to the outside and so there is less energy that your heating system has to make up for.

When we put our minds to it, we can think of a few conceivable effects that might modify one's personal decision about turning the thermostat down. If you have to get up in the middle of the night and you really, really hate a chilly house, then (for you) it might be worth the extra cost to keep the house warm all night. Or, with electric heat, it might be that you have to pay a higher rate in the early morning - when you're warming the house back up - than you do in the middle of the night.

But those are just quibbles. The basic point remains that in order to decrease the total amount of energy your heating system has to supply, TURN DOWN THE THERMOSTAT AT NIGHT!

One might say that heating a house is about the most inefficient process anyone could think of. You're not raising heavy objects, turning a motor, or lighting lights - all you're doing is replacing losses. Following that idea a bit further, since the losses you have to replace would be less if you had better insulation, the limiting case of a "perfect house" would be one with extremely thick walls; you would keep it warm by waiting for a day in September when the outdoor temperature is what you like as an indoor temperature, open all the windows for a while, and then close up the house until spring. That limiting case is obviously silly, if only because people (and their computers and stereos and stoves) heat things up and we also need fresh air to breathe. Nevertheless, the general lesson that better insulation leads to lower heating costs is clearly correct.