Space heaters are designed for households, which means they are safe for your house. With that being said, they are still not completely safe and you should always take precautions.
For instance, don’t leave your heater running on for too long without a break, especially if it doesn’t have an overheat protection switch or a timer. Also, you shouldn’t let your pets and kids go too near the heater, especially if it doesn’t have a cool exterior.
Furthermore, try not to leave the heater on overnight as you sleep. Even though the chances of the worst happening are pretty low, since most heaters come with timers and safety switches, you should still try not to be asleep as your heater runs.
For further ensuring safety, read through the instruction manual of your heater for guidance on how you can safely use your heater.