Mine used to be OK with the door closed, when I had an electric cooker with a grill in. I have a gas cooker with a separate eye-level grill now.
This reminds me how much I loathed having a cooker with the grill inside. Such a PITA, especially if you wanted to bake AND grill at the same time. (EG, oven chips and fish fingers.)
Much prefer the eye level grill.