(For what it’s worth, I wrote a Ph.D. dissertation on this topic.)
TL;DR: The most likely explanation is that the energy in the very strong magnetic field in the corona is being transformed into heat.
In plasmas like the solar corona, you can think of the magnetic fields (and the ionized gas, or plasma, attached to the fields) as being like elastic bands. Convection beneath the surface of the sun causes twisting of the magnetic field lines, building up stored energy. Eventually, in some regions of the corona, very large electrical currents are able to flow, leading to a rapid dissipation of the magnetic energy and a relaxation of the tension in the magnetic fields. This energy goes into heating the particles, leading to the hot corona. The corona is very tenuous, so it doesn’t take a lot of heat to make the temperature much hotter than the underlying chromosphere and photosphere.
The specifics of how, why, and where the current flows are still not fully understood and this has motivated several recent space missions. Also, the process by which magnetic energy rapidly transforms into heat (the process of “fast reconnection”) is an area of active and ongoing research.
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