Umm, no, just no.
That heater should have been installed to one side of the recept for a start.
I really "like" the idea of that cord running over the top of the heater, where, umm, all the HEAT comes out.
Electric work is so simple isn't it?
Is it a requirement in the US to use high-temperature flexible cord into a heating appliance?
Don't think that Romex is going to fly somehow.