Are you sure it's the oil heater? Is it an old oil heater? A big room?
My snake room is a 12 x 12 foot room in the basement. Two of the four walls are the foundation cinder blocks-no insulation and it has two windows that are garbage. I plan to insulate the windows this winter, but my bill only goes up about $30 a month from running my oil heater almost non-stop. I have it on a thermostat set to 75.