I have a new crown on my front tooth and there is a small gap in the gum on the distal side where the natural tooth extends beyond the crown edge and creates a ledge and I have a burning sensation. I am wondering how likely this exposed tooth is likely to decay? The dentist became angry and refuses to acknowledge that there is a problem.

You are definitely at risk for decay when there is a trap for bacteria to collect. Is your floss catching in that spot? If so, your dentist should have the lab remake the crown.