Understanding of thermophysical properties of complex liquids under various conditions is of practical interest in the ield of science and technology. Thermal conductivity of nonideal complex (dusty) plasmas (NICDPs) is investigated by using homogeneous nonequilibrium molecular dynamics (HNEMD) simulation method. New investigations have shown, for the irst time, that Yukawa dusty plasma liquids (YDPLs) exhibit a non-Newtonian behavior expressed with the increase of plasma conductivity with increasing external force ield strength F ext . The observations for latice correlation functions Ψ (t) show, that our YDPL system remains in strongly coupled regime for a complete range of plasma states of (Γ, κ), where (Γ) Coulomb coupling and (κ) Debye screening length. It is demonstrated, that the present NICDP system follows a simple scaling law of thermal conductivity. It has been shown, that our new simulations extend the range of F ext used in the earlier studies in order to ind out the size of the linear ranges. It has been shown that obtained results at near equilibrium (F ext = 0.005) are in satisfactory agreement with the earlier simulation results and with the presented reference set of data showed deviations within less than ±15% for most of the present data points and generally overpredicted thermal conductivity by 3-22%, depending on (Γ, κ).