We have an oil heater in both rooms with little people - they are warm to touch but not so hot they burn you.

Are we talking the same kind of oil heater here?

Other child seems to be immune to cold but we think she's completely insane so we have an electric blanket on her bed on a timer, it goes from 7:30-9:30pm. She absolutely loves getting into a warm bed.

I find the big problem with the oil heater is certain small people adjust the settings. We have it on very low and she keeps either turning it up or off. We have duct taped over the controls.