You need to consider that some walls may contain water pipes. Not having those warmed up sufficiently could lead to a bursted pipe, which could lead to significant damage.
Adding to what others have mentioned, you probably don’t use the same type/source of heat for the full house. A typical space heater is resistive heat, which is simply turning electrical energy into heat energy (at 100% efficiency). Your central heat could be a Gas-powered furnace (converting chemical energy to heat energy at ~90% efficiency), heat pump (converting electrical energy to heat at 300+% efficiency), or a few other options.
In my area, gas is much cheaper per joule than electricity. it ends up being the same price to heat the entire place with gas as it would be to heat just a room with an electric space heater. If I were to use a kerosene space heater, or a heat pump, or whatever else, then the numbers would change.
Yes, basic math says it uses less energy to heat a smaller area than a larger one. But that’s assuming the same type, cost per unit, and efficiency. This is unlikely unless you have the worst option on both (resistive electric heat)
Lovely reply; this is not the simplest answer but it’s the truth.
Please consider moisture (=mold) depending on humidity levels where you are. For example if you have one warm room the air will cool on the uninsulated interior walls to the next room, cooler air can not contain the same amount of humidity so this will condensate on (or in!) your walls. This is a good way to grow mold and get all kinds of expensive health issues.
You may not use the space, but you likely have water lines that can’t handle freezing temps, and other electronics/appliances that assume living space (non condensing humidity being important)
Now, setting your thermostat lower and only heating the room you’re in? Maybe. Whole house systems are damn efficient, so if you’re moving around the house with the heater, that’s a no go, but if you hang out in one closed door room, it’s an experiment you might want to try.
Expect the bathroom to be colder than you’d like if you’ve spent the day in your bedroom/office.
