I am just trying not to leave my DeLonghi heater alone in the room. I have a pet that can knock the heater over. But I leave it on when I go to sleep. It has an in-built timer so it shuts off automaticallly after several hours. (
https://pickadvisor.org/best-space-heaters-for-basement/ )I don't have a story with a furnance firing up , but once our microwave oven was left unattended, when my grandmother just set the timer for several hours (!) to warm up her food and forgot about it. Fortunately, that day I came home earlier from work and turned it off. Everything was fine, but the plate was burnt black and smelled smoke.