You can leave an oil-filled radiator on overnight in some circumstances as long as it lacks an exposed heating element and is designed not to get too hot. However, there is always a small risk of fire. But you can lower that risk if you ensure your children and pets don't have access to the heater. Also, it would be best if the radiator has in-built safety features, such as timers and anti-tilt sensors, that shut it off when it tilts or experiences any other issues.