This is a question that I think about every winter when it is time to spark up the furnace. Our furnace is controlled by a programmable thermostat. Do I save heating costs lowering my furnace at night and during the time I am at work? A furnace inspector told me that any potential saving are lost because the reheats are expensive and that you may as well keep the house at 68F all day and night. This does not sound logical to me because it depends on how long the house is kept at a lower temperature. If the temp is lowered to 58F for only 1 hour then there may not be any gain but if it is lowered for 8 hours then there may be a gain.
By the way, we have a modern high efficiency furnace. Are we gaining anything by lowering the temp to 58F at night and during the day?
This is a very frequently asked question. Yes you save money. Ask your furnace inspector why he doesn’t know this.
Some recent threads, which have links to other threads too:
http://boards.straightdope.com/sdmb/showthread.php?t=348692&highlight=thermostat
I have a post in here with about 3 other links:
http://boards.straightdope.com/sdmb/showthread.php?t=339135&highlight=thermostat
Just remember that when you heat a home, what you are doing is replace the heat lost to the world. The heat loss is proportional to the termparature difference (things like insulation change the proportionality constant, but that basic fact remains). This is integrated over the time. The lower the house temperature, the less heat loss. During reheating you are replacing the heat lost, that is all. Lower temperature means less heat means lower heating bill. Even for an hour it will make some difference. Not a lot, but some. If you are out of the house say from 8 to 6 every day and you have the thermostat turned down to 58 from 8 to 5, you will definitely save on heating costs. Just think in terms of heat escaping from the house, not in terms of reheating cost.
It is amazing how many otherwise intelligent people believe the opposite.
He probably does know it. But he works for the gas company, and your ‘saving heating costs’ means less income to his company. So he doesn’t have much incentive to push it.
It may be different in your area, but around here, most of the furnace inspectors are either employees or contractors to the gas company.
While the gas company in my area does offer to do furnace inspections, I would have to say the vast majority of inspectors are private companies who do it as part of general home inspection services.
And some are pretty knowledgeable, true - a couple of retired Engineers I used to work with became home inspectors.
Disclaimer: I am trying to make a career out of this, but I am not yet licensed. Take my words with a grain of salt, and check my math. 
Yes, you’ll save. The lower you set the temperature when you are away, the more you’ll save. You’ll pay an additional amount, though, to rewarm the house and its contents to normal room temperature when you return and want to use them.
Imagine keeping the house cool for longer and longer periods of time. As the cool periods get longer and longer, there’s a point where the energy savings from keeping things cool more than compensate for the extra cost in rewarming.
This can be figured out using standard building-science techniques.
Calculate and measure the areas of the (insulated) walls, floors, ceilings, and window areas. Find their aggregate thermal resistance using the R-values of the various materials. Plug in the temperature difference between your desired room temperature and the outdoor temperature, and you can find the steady-state flow of heat required to keep the room at a constant temperature. This is the minimum rate of flow that your heat source needs to supply to keep things from becoming colder.
With a lower room temperature (or higher outside temperature, for that matter), heat escapes at a slower rate, and you need to supply it at a slower rate.
Calculating the cost of rewarming is a little trickier. Rewarming is actually somewhat separate from heat escaping; it deals with ‘charging’ the contents of the house with a given quantity of heat energy, which raises the temperature of everything and more-or-less stays put (until it escapes to the outside).
To do it theoretically, you need to find out the heat capacity of all the materials inside the insulated shell of your house: interior partitions, drywall, books, furniture, etc. Then you plug in the difference between the starting and desired ending temperature, and you get a quantity of energy that you need to supply.
Furnaces and such are rated by their rate of supply of heat energy, so you can divide the amount of energy you need by that rate to find out the time it will take to warm things.
You can also use the costs off your electricity or gas bill to find out how much it will cost to rewarm your house each time as well as to find the cost of replacing the steady leakage of heat.
Yes, these things are calculatable, but it is often easier with an existing setup, such as an existing furnace and house, to just let the thing operate for a year and keep records, or even experiment, and then you know how much it costs, and you can even back-calculate to find out some of these quantities.