  Effects of collective modes on thermoelectric properties of a charge density
system is studied. We derive the temperature dependence of thermoelectric power
and thermal conductivity by applying the linear response theory to Fr\"ohlich
Hamiltonian. Energy dissipation has been attributed to non-linear interaction
between phase mode and amplitude mode, ignoring disorder effects. We have found
that the temperature dependence of the correlation function of electrical and
heat currents is the same as that of electrical conductivity. This implies that
thermoelectric power is inversely proportional to temperature. We have also
found that temperature dependence of all the correlation functions are
essentially determined by the common mechanism - nonlinear amplitude-phase
interaction. Thermal conductivity has nearly constant value at the temperature
above amplitude mode gap, and has exponentially low value at the temperature
sufficiently below it.
