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Most Americans are likely paying more to heat their homes this year than they did last winter, according to the Energy Department, because temperatures are expected to be lower than last year and oil and natural gas costs have risen. A programmable thermostat can help counteract those high utility bills. But what about smart, Wi-Fi-enabled thermostats, such as those made by Nest, EcoBee3, and Honeywell? Do their extra features deliver enough extra energy savings to justify a price tag of up to $250? The answer may depend more on you than on the device.

Related: 50 Ways to Save Energy (and Money) This Winter

Consumers can knock as much as 10 percent off a heating bill by lowering the thermostat 7 degrees to 10 degrees when away from home for eight hours at a stretch. This sounds great, but most people don't diligently turn the temperature up and down during their comings and goings. That's where a programmable thermostat comes in. The device lowers the temperature automatically during sleep hours or when the home is empty. Users can even customize the settings by days of the week -- for instance, by setting the thermostat to save energy during weekday business hours but keep the heat on over the weekend when people are home during the day.

For consumers with erratic work schedules (perhaps because they do shift work or travel frequently), reprogramming can be a pain. Top-end thermostats such as the Honeywell Smart Thermostat ($158 on Amazon) can help -- they are Wi-Fi-connected and can be contacted remotely when a routine changes, even just for a last-minute dinner or late meeting. The Honeywell learns how long it takes to get the temperature back up and kicks on in time to make the house comfortable when you walk in, removing the temptation to crank up the heat. The Nest ($250 at Best Buy) learns your habits and adjusts the heat based on usage patterns. The Nest and Ecobee3 ($237 at Walmart) also have sensors that detect movement in a home and drop the temperature when it's empty.

It may seem like such features would make it easy to save a lot of money (not to mention energy) in the long run -- certainly that's the claim of the manufacturers. But do the savings even make back the cost of the device?

It's hard to talk concrete numbers, because the amount it costs to heat (and cool) a home depends on many factors, including the type, age, and efficiency of the heating system; how well the walls, doors, windows, and ductwork are sealed; and the thermostat's location, among other things. A home with an old, inadequate heating system or that isn't well-insulated, for example, probably needs a more expensive fix than a $250 thermostat to start seeing significant energy savings. What's more, utility costs fluctuate, and if prices go up significantly, using less energy may cost the same amount of money. Climate also makes a difference. The Energy Department advises that consumers in regions with mild weather will see the most savings.

All that said, a Wi-Fi-enabled thermostat might indeed save money. Pacific Gas and Electric in California partnered with Honeywell to do a trial of smart thermostats, and found that people liked having an app to change temperature settings remotely and used the app more than they would have used the thermostat alone. More than half reported using less energy. An internal study at Nest found that most consumers saved 10 percent to 12 percent on heating and 15 percent on cooling. The savings averaged out to about $130 a year at the lower end, suggesting that in two years the Nest would pay for itself. On user forums, some smart thermostat owners also point to a "smart home" discount on their home insurance.

The users who seem to benefit most from a smart thermostat are those who replaced a manual thermostat or never properly programmed a previous thermostat. Using a regular programmable thermostat judiciously can save about $180 a year on household energy bills, according to the Environmental Protection Agency's Energy Star program -- no smart features necessary. But many Americans with programmable thermostats set them incorrectly -- in some cases just by leaving the clock set to the wrong time -- or don't program them at all, leaving potential energy savings on the table. A Lawrence Berkeley National Laboratory study concluded that some programmable thermostats are so complicated that they actually make matters worse. Wi-Fi-enabled thermostats pretty much idiot-proof the process.

By far the most important piece of the equation is the user. An expensive smart thermostat can make the programming process easier, or at least more appealing, and adjust easily to schedule changes. But if you have a relatively consistent routine and the discipline to effectively program a cheap thermostat, you may be able to realize similar savings without investing in a smart thermostat.