  Heat radiation and near-field radiative heat transfer can be strongly
manipulated by adjusting geometrical shapes, optical properties, or the
relative positions of the objects involved. Typically these objects are
considered as embedded in vacuum. By applying the methods of fluctuational
electrodynamics, we derive general closed-form expressions for heat radiation
and heat transfer in a system of $N$ arbitrary objects embedded in a passive
non-absorbing background medium. Taking into account the principle of
reciprocity, we explicitly prove the symmetry and positivity of transfer in any
such system. Regarding applications, we find that the heat radiation of a
sphere as well as the heat transfer between two parallel plates is strongly
enhanced by the presence of a background medium. Regarding near- and far-field
transfer through a gas like air, we show that a microscopic model (based on gas
particles) and a macroscopic model (using a dielectric contrast) yield
identical results. We also compare the radiative transfer through a medium like
air and the energy transfer found from kinetic gas theory.
