hi, that is a very hot topic for study right now. It is starting to be clear that the corona is heated in some way due to energy being transported from the lower parts of the solar atmosphere up. The solar magnetic field likely has a strong role in heating the Corona, either by releasing energy itself as it gets tangled up or by funneling some of the energy in the form of waves.

A Japanese spacecraft Hinode (the name means "sunrise") has made impressive observations about possible Alfven waves in the solar corona. You can read the story and see some movies from http://www.esa.int/esaCP/...ndex_0.html#subhead3