There are other ways for a space heater to cause a fire besides overheating. When I needed one to heat up the bathroom, I did a lot of research.
The first thing I did was pay a licensed electrician to replace my old outlet with a GFCI outlet that automatically shuts off power to it if it gets wet. Then, I found out that if the plug doesn't fit snugly in the socket, it allows "arcing" - which is sparks in the space between the metal prongs on the plug and the metal in the outlet. That causes the plug to get very hot - hot enough to start a fire in the wall. I always check the plug after the heater has been on for a few minutes. If it's hot, it doesn't fit snugly & it's arcing & can cause a fire.
I also had 10 other old outlets replaced after noticing the vacuum cleaner plug also got hot & didn't fit snugly in the outlet.
A space heater (and a hair dryer) use a lot of power - around 1500 watts.