I was reading the posts on electric heaters yesterday. When winterizing, I blow out my lines and pour antifreeze into traps an toilet. We live in upstate S Carolina and don't usually need more then ...
I think the cord getting warm is pretty normal, but the outlet on the wall should not be warm. If you feel proficient enough you could pull the receptacle out of the wall and make sure all of the screws holding the wires down are tight. I hate those push in type receptacles and would advise replacing them with screw type.