  Physical processes involving charge transfer, spin exchange, or excitation
exchange often occur in conditions of resonant scattering. We show that the
$s$-wave contribution can be used to obtain a good approximation for the full
cross section. This approximation is found to be valid for a wide range of
scattering energies, including high above the Wigner regime, where many partial
waves contribute. We derive an analytical expression for the exchange cross
section and demonstrate its relationship to the Langevin cross section. We give
examples for resonant charge transfer as well as spin-flip and excitation
exchange. Our approximation can be used to gain information about the $s$-wave
regime from data obtained at much higher temperatures, which would be
advantageous for systems where the ultracold quantum regime is not easily
reachable.
