The Corona of the Sun Is a Lot Hotter Than the Surface of the Sun, Right?

This is not like an equilibrium situation. In order for this to persist, you need some source of heat. But if the source of heat is the sun itself, you would expect it to be hotter in the core. So really nothing about this makes sense. There needs to be some way to heat the corona. And it doesn't seem like it can come from the inside, right? It's a very strange situation. Somehow heat seems to be flowing out, violating the second law of thermodynamics.