  To determine the electron heat flux density on macroscopic scales, the most
widely used approach is to solve a diffusion equation through a multi-group
technique. This method is however restricted to transport induced by
temperature gradients without accounting for other sources of fast electrons
because the electric field induced by the charge separation is indirectly
treated. In addition, significant discrepancies are reported on the underlying
distribution function when compared to complete kinetic calculations. These
limitations motivate the research for alternative reduced kinetic models. The
physical content of one of them is here deepened, its precision improved and
the benefit of its usage compared to other models discussed.
