If you have a furnace your home is heated by forcing heated into the home through ductwork. The air is heated by passing it over a heat exchanger. The heat exchanger can be fueled either with gas or electricity.
Having a programmable thermostat which will turn the heat down during the day when you are away from home or at night when you are asleep can result in savings. The heat exchanger does not need to run as much to heat as much air as would be needed if you were home and needed the home warmer. It can switch off during the times when the home does not need to as warm.
If you have a heat pump, a programmable thermostat is not your friend. A heat pump recirculates heat from outside the home to inside and vice versa. It does not generate heat from scratch. How does this work in the winter when it is cold outside? How is your heat pump supposed to make the air inside the home warm?
Perhaps you might remember high school physics? Pressure is directly proportional to temperature? Gay-Lussac’s law? If you pressurize a gas into a container, it heats up. Think of pumping air into tires, pumping air into them gets the tires warm. Conversely, if you spray whipped cream out from the canister onto your waffles, the can gets cold.
Same deal with the refrigerant in your heat pump system. When in heating mode, the refrigerant is forced to expand by reducing the pressure on it, this causes the temperature of the refrigerant to drop. This creates a heat differential between the outside air and the coils of the heat pump. Heat flows from hot to cold, heating up the air which is then piped into your home.
What if the air outside is very cold, so cold that it is almost the same temperature as the expanded refrigerant? This is when the auxiliary heat comes in. Heat pumps have electric strips that will generate heat when there is not enough differential in temperature to heat your home.
So, what is the connection with a programmable thermostat?
Getting the refrigerant to expand takes energy. You heat pump works most efficiently if the refrigerant is set at the same temperature. Changing the temperature of the refrigerant is what consumes energy. If your programmable thermostat is busy flipping the temperature up and down multiple times a day, your heat pump struggles to keep up, using a lot of energy, thereby increasing the your utility use and hence your bills!
So contrary to what you may think, using a programmable thermostat can actually cost you more money if you have a heat pump.