Basically any type of electrical appliance can possibly spark a fire at any time if the stars align, but that doesn't mean you don't use refrigerators and lamps, right? Space heaters are fine if you buy a good one and use them correctly. Here's some info:
We use an electric space heater in DD's room at night. Ours does't get super hot to the touch, but it does get hot. Basically I don't let her down on the floor in the morning on her own. I take her right to the changing table to change her diaper and get dressed, then out of the room for breakfast. She's never on the floor with it when it's hot.