Tim

An excellent question.

First off - space heaters draw up to about 10 amperes - so fires at poor connections at the outlet can be a problem.

But as for the heater - these would be rare. If a heating element is exposed, and you can get a Class A combustible on it (straw paper etc) you can ignite the material. Otherwise, good luck... there is a tilt switch in most heaters - if it is placed face down on a carpet or rug or whatever, heat flux accumulates and the unit shits down. Throw a towel over it - it shuts down.

The heaters always have a plethora of warnings - like keep 18" away from combustibles. The implication is that at 17" or so you can cause a fire - doesn't happen. You can have stuff 1" in front of the heater and it will not be ignited.

How good are the safeties? In Wise County about ten years ago, a man tried to murder his wife with a space heater. He bypassed every safety on the heater, placed it face down on a pile of clothing in the trailer house, and left it to kill his wife. Problem - she knew of the threats and had left. The trailer burned down. The wife told the sheriff, who sent in the heater for analysis. Sure enough, the bypass wires were present on the t-stat and the safety. Husband plead out to attempted murder.

We have seen two other arson fires from space heaters - persons poured gasoline on them in warm weather during the day; at night it gets cool and the arcing contacts on the thermostat ignites the vapor when the t-stat cycles...

Go spend $30 and experiment with one... throw a towel on it, etc. you will be surprised as to how well these heaters work.