I have one of those oil heaters, they're still very hot to the touch and were not very good at heating up my room evenly, so I switched over to a ceramic heater with a fan that oscillates and has automatic temperature control.
I prefer the ceramic heater.
This is something similar on amazon. https://www.amazon.com/Lasko-CT16450-Oscillating-Thermostat-Protection/dp/B08KSJZW4T
https://www.amazon.com/gp/product/B08KSJZW4T/
I have two of these space heaters and they can heat my whole house. not super expensive either. just in case it keeps getting dragged out.