A resonant scattering of hard synchrotron radiation and neutrons by nuclei in a crystal is considered a t a recoil energy of R > hi;, and the lifetime of the compound nucleus to rn 2 4 6 , with I5 being the characteristic phonon frequency. In these cases the main contribution to the scattering is made by the secondaryparticles emitted in the relaxation process of the recoil energy of the compound nucleus. This emission is called hot nuclear fluorescence (hot emission of neutrons). Numerical calculations are performed to show the strong dependence of this type of resonant scattering spectra on the parameters R/h6: &to, and local lattice dynamics. The requirements for the corresponding experiments, following from this study are considered. A possible set-up for an experiment is proposed which allows to study the hot nuclear fluorescence without spectrometer.