  The unusual Raman spectrum of MgB$_2$ and its formidable temperature
dependence are successfully reproduced by means of a parameter-free \emph{ab
initio} nonadiabatic theory that accounts for the electron-hole pair scattering
mechanisms with the system phonons. This example turns out to be a prototypical
case where a strong nonadiabatic renormalization of the phonon frequency is
partially washed out by the aforementioned scattering events, bringing along a
characteristic temperature dependence. Both electron-hole pair lifetime and
energy renormalization effects due to dynamical electron-phonon coupling turn
out to play a crucial role. This theory could aid in comprehending other Raman
spectra characterized with unconventionally strong electron-phonon interaction.
