We claim that there is an additional contribution to the thermal condu
ctivity in excess of the normal phonon and free carriers contribution
in charge-density-wave (CDW) systems below Peierls transition which we
attribute to the phase oscillations of (CDW) order parameter. We demo
nstrate for two chosen CDW systems, K0.3MoO3 and (NbSe4)10I3, that the
observed increase in the thermal conductivity corresponds to the temp
erature range where the screening of the Coulomb interactions is suffi
cient to allow the contribution of the weakly damped phasons with larg
e velocity.