While considering using one of the rooms in my home for the scale kids I noticed one key factor when window shopping for oil heaters. Some are rated to handle a specific room dimension. Maybe look and see if the current heater can handle the size of the room. You can also block the bottom of the door (from the outside) with a small draft trim to aid with temp retention so that the unit doesn't need to run hotter, thus not working a thermostat to hard. If you have one, slap a kil-a-watt inline with the stat to get an accurate usage reading. Those things are so freaking handy! Just a few things I've jotted down when I'm ready to dedicate a room. Good luck...

What heater do you have and what is its rating?
Keep in mind that an average home will be wired from 15 to 20 Amp breakers for different rooms.