Lead Chalcogenides (PbS, PbSe, PbTe) are the important class of materials and are the best thermoelectric materials in the mid temperature range (~700K). In the present work, samples of Cu_xPb_(1-x)S (x= 0, 0.2,0.4,0.6 and 0.8) were prepared in order to tailor its thermal conductivity (k ) for thermoelectric applications. Lowering the thermal conductivity is the most focused way to obtain high performance of thermoelectric material. The temperature dependence thermal conductivity of Cu_xPb_(1-x)S (x= 0, 0.2,0.4,0.6 and 0.8) samples has been investigated in the temperature range of 300 K to 700 K. The reduction in thermal diffusivity (α) and thermal conductivity (k) were observed for the Cu_xPb_(1-x)S (x=0.2,0.4 and 0.6) samples compared to pure PbS sample in the entire temperature range of study. At room temperature the thermal diffusivity and thermal conductivity of the Cu_xPb_(1-x)S (x=0.2,0.4 and 0.6) samples were found to be ~4.0 and 3.0 times lower than that of PbS respectively. The presence of natural hierarchical scattering centres of different length scale in the Cu containing PbS samples exhibits extreme low thermal conductivities of 1.25 W/mK at 560 K.