The thermal radiation of lossy media is described by a random current‐source term that is introduced into Maxwell's equations. The media treated are linear, in general anisotropic, nonuniform, and such that the constituent relations are not local relations, but are described in terms of a Green's operator. For such media, in thermodynamic equilibrium, it is shown that simple relations exist between the correlation and spectral density matrices of the random current‐source field and the Green's conductivity operator. These relations are analogous to Nyquist's theorem of lumped circuits.