Thermostats can provide significant energy savings.
A manual thermostat can be all you need if you are willing to actively manage its settings in a regular basis.
But if you haven’t the time or the will, or if you have a sophisticated heating and cooling system and a large house, a programmable thermostat is more than just a mere convenience.
See: Programmable vs. Manual vs. Wireless Thermostats
Set up your programmable thermostat correctly; otherwise energy savings will be small, or you may even increase your energy consumption.
Consider the ideal winter (68ºF/20ºC?) and summer (78°F/26° Celsius?) temperatures, and how much you want to vary these temperatures for when you are out or sleeping.
See:
Thermostat Settings for Cooling
Thermostat Settings for Heating
Most programmable thermostats cost between $40 and $100 and are relatively easy to install.
Since thermostats use low-voltage wiring, replacing a thermostat with a new one is a straightforward task.
Be aware anyway. Manufacturers may require professional installation, and warranties will depend on it. On the other hand, installation should be done properly. An incorrect installation can damage not only the thermostat but also the HVAC equipment
See:
Thermostat Installation and Wiring
Many modern programmable thermostats are quite sophisticated, with many features. Most of them are important for ease of use or convenience, though irrelevant for energy efficiency.
See:
Thermostat Features
Thermostat Buying and Prices
Super-insulated homes, with top windows, and a good design and orientation to the sun and elements, may not need central heating and cooling systems and... thermostats.
See, for details:
Thermostat & Energy Savings
The idea sounds great. Why not limit heating and cooling to the rooms that are being used? Why heat the entire house when we are using only one or two rooms? That’s the idea behind zoning: to heat and to cool the rooms according to their use, occupancy and needs.
Zoning is critical for energy savings, in harsh climates, namely in large buildings with conventional levels of insulation. And thermostats – namely wireless thermostats - are a key part of zoning.
See: Temperature Zoning for Energy Efficiency
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House-Energy Video on Thermostats: