The thermal conductivity of complex fluid materials (dusty plasmas) has been explored through novel Evan-Gillan homogeneous non-equilibrium molecular dynamic (HNEMD) algorithm. The thermal conductivity coefficient obtained from HNEMD is dependent on various plasma parameters (Γ, κ). The proposed algorithm gives accurate results with fast convergence and small size effect over a wide range of plasma parameters. The cross microscopic heat energy current is discussed in association with variation of temperature (1/Γ) and external perturbations (Pz). The thermal conductivity obtained from HNEMD simulations is found to be very good agreement and more reliable than previously known numerical techniques of equilibrium molecular dynamic, nonequilibrium molecular dynamic simulations. Our new investigations point to an effective conclusion that the thermal conductivity of complex dusty plasmas is dependent on an extensive range of plasma coupling (Γ) and screening parameter (κ) and it varies by the alteration in these parameters. It is also shown that a different approach is used for computations of thermal conductivity in 2D complex plasmas and can be appropriate method for behaviors of complex systems.