No-one really knows is the short answer. It is a bit of a problem. I think it is down to about two possible candidates. Magnetic reconnection and/or wave heating. I think. I have a book on it somewhere I will check and correct if I have got that completely wrong! :)

From NASA: http://www-spof.gsfc.nasa.gov/Education/wcorona.html The source of the corona's heat remains a puzzle. It is almost certain that its energy comes from the Sun's internal furnace, which also supplies the rest of the Sun's heat. However, as a rule, temperatures are expected to drop the further one gets from the furnace, whereas the million-degree corona lies outside the surface layer where sunlight originates, whose temperature is less that 6000 C.

(Sorry for my chaotic writing) Why are sun spots dark? Why is the corona hotter than the surface? If the energy of the sun was emanating from the middle wouldn't the sun spot be brighter than the surface. I am no physicist but I've learned that heat travels from hot to cold. How then could heat-energy from the center of the sun skip the surface and jump into the corona? This is not logical. Maybe we all have it wrong. What if the opposite was at work here. What if the energy was coming from outside the sun, manifesting at the corona and sometimes bursting through the surface causing sun spots. Nicola Tesla once proposed pulling out free energy from the sky. What if we lived in an electric universe and gravity was not the dominant force of the cosmos. Cosmologist search for a theory of everything but we don't even know what 90% of the universe is made of. We are a young civilization. When I was little I remember being told that electrons and protons were the smallest constituents of matter, yet we keep finding new particles and smaller stuff. Galaxy NGC 7603, why are we getting different red shift measurements from two objects that are obviously connected by plasma. Something is wrong with our scientific foundation and unless we as humanity are willing to wipe the slate clean when new evidence and experiments show us a new way of thinking, we do ourselves a disservice and all our theories of Big Bangs and quantum theories become nothing more than dogmatism. The Big Bang, how can something be created from nothing? In String theory, what are these vibrating strings made of? If you say energy or some other fundamental state of consciousness, then I would ask, what then is it made of. Logic tells me the answer cannot be nothing. The universe is infinite, not only in space-time but infinity of the big and small. In its infinity, we are life because life seems to be the only thing that give things order. Order of the stars and of the atomic. We may very well be the atomic makeup of a grander life form. Therefore life is infinite. Maxwell Crone