Never leave a space heater unattended. Turn it off when you're leaving a room or going to sleep, and don't let pets or children play too close to a space heater.
It is perfectly safe to leave your gas heat/furnace on while you're away at work and overnight. Rather than turn it off, you might want to consider a programmable thermostat to lower the temperature while you are both away at work and sleeping, and then bring it up to an acceptable temperature while you are home.
Absolutely. The US Department of Energy records about 25,000 house fires every year that are linked to a space heater fire.
Fire Hazards
 If the unit is left unattended or placed too close to flammable materials, such as curtains or bedding, it can ignite and lead to a devastating fire. To avoid this danger, always keep a clear distance of at least three feet between the heater and any combustible objects.
During the Day: It's safe to leave your heater on for 6-8 hours if you're in the room.
What is the safest heater to leave on overnight? While it's not recommended to leave any space heater on if you're not monitoring it, oil-filled, radiant space heaters are considered safer than ceramic convection (hot air) types, according to Roberson. Both of these options are safer than open-coil heaters.
Fires are one of the biggest risks associated with leaving electric heaters on all night. If an electric heater has frayed wiring or malfunctions, then there is a high chance of it igniting. Electric heaters also make the air in the room really dry by conducting a lot of heat.
Avoid the carbon monoxide poisoning by turning off the heater and unplugging it before leaving the room or going to the bed. Signs of too much carbon monoxide in the rooms include headache, dizziness, abdominal pain, discomfort, vomiting, nausea and weakness.
Plug the heater directly into an outlet. Do not plug a heater into an extension cord or a multi-outlet strip/ surge protector. Place the heater so there is a 3-foot safety zone: not under your desk, nothing is draped over it and 3 feet away from curtains, blinds, hanging materials, boxes and piles of paper/plastic.
Leaving electric heaters on overnight is not recommended. Leaving a heater unattended for any length of time increases the risk of fire. For wall-mounted electric radiators, it's vital that all curtains and other combustible materials are kept well away from.
You Should Not Leave Space Heaters on Unattended.
Turning the heat on by itself typically does not cause a fire. Modern heating systems, such as central heating systems or electric heaters, are designed with safety features to minimize the risk of fire.
Place space heaters on a solid, flat surface. Keep them at least three feet from things that can burn. Check your space heater for cracked or damaged cords and plugs. Plug space heaters directly into wall outlets, don't use an extension cord or power strip.
Running Your Heating System Continuously May Be a Good Idea
 It isn't bad to run your heating system on a 24/7 basis if outdoor weather conditions demand indoor warmth.
You can leave them on indefinitely. I have one in our upstairs bathroom that I never shut off. It has a thermostat that keeps a very even temperature. The benefit of an oil-filled radiator type heater is that it never gets hot enough to ignite drapes or paper.
Whether you'll be gone for the day at work or you're going on a several-day vacation, you may be wondering, “Should I leave heat on when away?” In general, the answer is yes. It's best to leave your heat on despite the high costs, but you can still save money.
Portable electric heaters are high-wattage appliances that have the potential to ignite nearby combustible materials like curtains, beds, sofas, paper, clothing, and flammable liquids. If ignition results from a heater left on and unattended, a major fire could result. damaged.
Keep heaters at least three feet away from flammable materials like paper, trash bin, furniture, drapes or carpet. Even though electric space heaters do not have an open flame, the heating elements of some types of electric heaters are hot enough to ignite nearby combustibles.
4. It's a Fire Hazard. Leaving your electric heater on all day is also a fire hazard. If you are not home to monitor the heater, it could overheat and start a fire.
Leaving the heater running all night might cause a fire because of an overloaded circuit, or a nearby item could ignite. Some older portable heaters might not be designed with the same safety features as a more modern heater.
Never leave a space heater running for long periods of time, and especially not overnight; it is best to use them intermittently; depending on your situation, a suggested practice would be to turn it off/unplug it for 10 minutes every hour if you depend on its use for longer periods.
Never leave a space heater unattended. Turn it off when you're leaving a room or going to sleep, and don't let pets or children play too close to a space heater.
Leaving your home's furnace running day and night is expected and fully safe to do. However, many homeowners also use alternative heating systems, including space heaters and electric heaters, which are not safe to use when unattended (like at night).
The good news is that modern infrared heaters are very safe to use even when left unattended during the night, even while you are sleeping.