[en] One of the most convenient methods to obtain information about the energy distribution function of electrons in conducting materials is the measurement of the energy resolved current $j(\omega)$ in field emission (FE) experiments. Its high energy tail $j_>(\omega)$ (above the Fermi edge) contains invaluable information about the nature of the electron--electron interactions inside the emitter. Thus far, $j_>(\omega)$ has been calculated to second order in the tunnelling probability, and it turns out to be divergent toward the Fermi edge for a wide variety of emitters. The extraction of the correlation properties from real experiments can potentially be obscured by the eventually more divergent contributions of higher orders as well as by thermal smearing around $E_F$. We present an analysis of both factors and make predictions for the energy window where only the second order tunnelling events dominate the behaviour of $j_>(\omega)$. We apply our results to the FE from Luttinger liquids and single-wall carbon nanotubes.