Safety first. There is no manufacturer that will recommend any other fuel to be burned in its kerosene heater other than kerosene. That doesn't mean it can't be done, but neither this article nor any manufacturer will recommend that it should be done. However, there is a type of heater on the market that will burn a variety of petroleum-based fuels, and it is actually manufactured to do just that, safely.
This is for basic information only; heating or any other type of oil should not be burned in a kerosene heater.
Kerosene is a light grade of diesel oil, or No. 1 as it is known in the trade. Heating oil, which is classified as No. 2, is heavier and less combustible than kerosene. When burned in a kerosene heater, heating oil will smoke and emit noxious fumes. Additionally, it will leave unburned deposits on the wick and burning mechanism, requiring increased cleaning and maintenance. Thus, while heating oil may work in a kerosene heater, it hardly seems worth the trouble.
Alternative Fuel Burners
Most waste oil heaters will burn any kind of petroleum product. However, the heaters are designed to burn waste oil. Burning heating oil in one is like powering your lawn mower with high-octane gasoline.
A better solution is a Petromax heater. It is designed to burn various clean, refined petroleum products by merely changing the nozzle.