The Brillouin linewidths of longitudinal phonons (q//e// left bracket 1, 0, 0 right bracket ) and soft transverse phonons (q// left bracket 1, 1, 0 right bracket ; e// left bracket 0, 0, 1 right bracket ) were measured for the first time in KCN in its cubic phase above the elastic phase transition temperature. A semiphenomenological model is proposed which explains the temperature variation of both these linewidths and of the related elastic constants, and, in particular, the absence of any spectacular variation of the transverse phonon linewidth close to the transition in spite of the soft character of the related elastic constant.