The Sun's corona is millions of degrees Kelvin hotter than the main body of the Sun (reaching temperatures of up to 10 MK). A number of possible mechanisms have been proposed to explain why. They include:
- fast and slow magneto-acoustic body waves
- Alfven body waves
- slow and fast magneto-acoustic surface waves
- current (or magnetic field) dissipation
- mass/particle flows and magnetic flux emergence.
As yet, none has been confirmed as the cause.
Further reading http://solar-center.stanford.edu/FAQ/Qcorona.html
Note: In 1997 the Goddard Space Flight Center issued a press release regarding a new 'Magnetic Carpet' theory. More up-to-date detail needed on this