That is a good question about the sun's corona, one that even most astronomers are not sure of today. The surface of the sun is about 5000 degrees, but the corona, just outside the sun, is around a million degrees. Although there is no clear answer, a current theory is that the corona is heated by magnetic fields we see on the surface of the sun.

If you've ever done the experiment where you place iron filings around a magnet, you may have noticed that magnets (which have a North and South pole) have a field that starts at one pole and ends at the other. There is a rule that magnetic field lines can not cut through each other - but when these magnetic surfaces form on the sun, the fields lines get very close to each other, and when they get too close they have to move to avoid cutting. When the magnetic field lines move, they give off lots of energy.

I think the short answer is that no one knows for sure. The corona is very diffuse so there is plenty of energy available to keep it hot but we don't understand the mechanism for transferring energy to the corona and keeping it hot.