This is absolutely a great way to save money in the winter for the reasons you describe. If you have a space heater and run it in only a room or two, then keep the thermostat in your home quite low, you’ll save a ton on your energy bill.
For example, in my own home, we use this 1,500 watt space heater.
Most of the time during the winter, particularly on weekends, we let the whole house stay cool and keep only the family room warm. When we switch to this mode, we turn the thermostat down to about 45 degrees, which is cool enough that the furnace virtually never turns on.
Then, we all settle into the family room. When we notice it getting cold, I’ll flip on that space heater full blast for a while, using 1,500 watts for about ten minutes until the room is warm. Then I’ll turn it on really low, where it uses about 200 watts, and this – plus our body heat – keeps the room we’re in pretty warm.
So, let’s compare that for a 24 hour day against the use of our furnace.
With normal furnace usage, we’ll leave the house set at about 60 degrees Fahrenheit. We wear long sleeves and pants during the winter, so this feels fine. We have an approximately 25 kW furnace (based on the information I could find on the labeling, which is appropriate for a house of our size in a cold climate), which flips on for about ten minutes per hour, on average (I’ve measured it on cold winter days).
Thus, over the course of a full day, our furnace will run for four hours. With a 25 kW furnace, that’s 100 kWh of usage, or about $12 in energy use.
With a space heater, over that same period, I would run it at 1,500 watts for about 10 minutes, then at 300 watts permanently afterwards. That totals approximately 75 kWh of usage, or about $9 in energy use.
In other words, if we are going to spend most of the day in the family room, we’ll save dollars by turning the furnace very low and just heating the family room with a space heater. (At the end of the day, we’ll often go upstairs and position the space heater between the bedrooms at a fairly low rate and it keeps us quite warm during the night while the rest of the house is cool.)
For us, that savings is about $3 a day, according to my math.
However, the variables for your situation are large. How big is your house? How cold is your climate (generally, furnaces in colder winter climates tend to have higher wattages)?
Perhaps most importantly, how much of a difference is there between the area you want to heat via space heater and the area you want to heat via furnace? If you’re living in a small apartment, for example, or have a house that’s less than 800 square feet or so, you’re probably not saving much at all with a space heater.
The savings kick in if you have a large house and are only heating one room with a space heater and if you live in a climate with a large difference between indoor and outdoor temperature.