  We present here a generalization of the thermal discrete dipole approximation
(TDDA) that allows us to describe the near-field radiative heat transfer
between finite objects of arbitrary shape that exhibit magneto-optical (MO)
activity. We also extend the TDDA approach to describe the thermal emission of
a finite object with and without MO activity. Our method is also valid for
optically anisotropic materials described by an arbitrary permittivity tensor
and we provide simple closed formulas for the basic thermal quantities that
considerably simplify the implementation of TDDA method. Moreover, we show that
employing our TDDA approach one can rigorously demonstrate Kirchhoff's
radiation law relating the emissivity and absorptivity of an arbitrary MO
object. Our work paves the way for the theoretical study of the active control
of emission and radiative heat transfer between MO systems of arbitrary size
and shape.
