  We investigate the question of the proper thermal averaging of neutralino
annihilation amplitudes which possess poles and thresholds, as they impact on
the calculated neutralino relic density and therefore on the cosmological
viability of supersymmetric models. We focus on two typical resonances, namely
the $Z$ boson and the lightest Higgs boson ($h$). In the context of
supergravity models with radiative electroweak symmetry breaking, an
exploration of the whole parameter space of the model is possible and the
overall relevance of these sophisticated analyses can be ascertained. As an
example we chose the minimal $SU(5)$ supergravity model since the presence of
such poles is essential to obtain a cosmologically acceptable model. We find
that the proper thermal averaging is important for individual points in
parameter space and that the fraction of cosmologically acceptable points is
increased somewhat by the accurate procedure. However, qualitatively the new
set of points is very similar to that obtained previously using the usual
series approximations to the thermal average. We conclude that all
phenomenological analyses based on the previously determined cosmologically
allowed set remain valid.
