If you want just a space heater, EdenPURE is pretty good and it's VERY child-safe. It seems a little spendy at first but it warms a room very well without overheating it and it remains cool to the touch. You can warm a few rooms with it, actually. They don't take up a lot of space. When our oil is low we use our EdenPURE. I was hesitant about getting one, but my husband was insistent because oil prices can be so outrageous, but honestly the electricity ends up being about the same if you were to use it nonstop without ever turning either off.
It's very quiet with just a low hum, and it doesn't blast hot air. It has two warmth settings.
I have a daughter with Autism and Sensory Integration Disorder and she loves this heater. She says it's gentle.