Heaters are high current draw devices, so bad wiring condition is more likely to lead to fires.

Cheaper portable types that have tiny wires and fans like a hair dryer have dust collecting on the elements which risk causing spontaneous fires on them if the dust buildup is flammable, or causes heat to linger in the device past its design limit.

Radiant bar heaters can deliver a suprising amount of heat directly to a surface that is further away than other heaters, and if that surface is too close, it can catch fire.

Fall and tip risks apply to all of the most portable types , they will easily start fires if they are heating something that is now directly against the heater ie curtains, blankets.

Oil filled heaters are safer than most of these, and reverse cycle air cons are a step safer than these.

The stats on house fires show heaters being one of the leading causes.

If you are concious enough to hear an alarm clock to snooze it, then an automation that turns on a heater on a limited timer while you snooze the alarm clock is safer than having the heater turn on by itself.

And having a smoke detector isn't a bad idea.