We have applied the dynamical jellium model for metal clusters, which treats simultaneously the vibrational modes of the ionic jellium background in a cluster, the quantized electron motion and the interaction between the electronic and the ionic subsystems beyond the adiabatic approximation, for the calculation of widths of electron excitations in metal clusters caused by multiphonon transitions, and investigated their temperature dependences. We have also estimated the decay time and the energy relaxation time of electron excitations in metal clusters.