  The question why the solar corona is much hotter than the visible solar
surface still puzzles solar researchers. Most theories of the coronal heating
involve a tight coupling between the coronal magnetic field and the associated
thermal structure. This coupling is based on two facts: (i) the magnetic field
is the main source of the energy in the corona and (ii) the heat transfer
preferentially happens along the magnetic field, while is suppressed across it.
However, most of the information about the coronal heating is derived from
analysis of EUV or soft X-ray emissions, which are not explicitly sensitive to
the magnetic field. This paper employs another electromagnetic channel -- the
sunspot-associated microwave gyroresonant emission, which is explicitly
sensitive to both the magnetic field and thermal plasma. We use nonlinear
force-free field reconstructions of the magnetic skeleton dressed with a
thermal structure as prescribed by a field-aligned hydrodynamics to constrain
the coronal heating model. We demonstrate that the microwave gyroresonant
emission is extraordinarily sensitive to details of the coronal heating. We
infer heating model parameters consistent with observations.
