The studies of strongly coupled complex plasmas are of significant in the area of science and technology. The plasma thermal conductivity strongly coupled (complex) plasmas is of significant in scientific technology, because it behaves as complex fluids. The two-dimensional (2D) plasma thermal conductivity of strongly coupled complex dusty plasmas (SCCDPs) has been investigated by using the homogenous nonequilibrium molecular dynamics (HNEMD) simulations, proposed by Evan-Gillan scheme, at higher screening parameter к. In our case, we have chosen particularly higher screening strength (к) for calculating plasma thermal conductivity. The new simulations of plasma thermal conductivity are computed over an extensive range of plasma states (Г, к) for suitable system sizes by applying the HNEMD simulation method at constant external force field strength (F * ). It is found that the plasma thermal conductivity of SCCDP S decreases by increasing plasma states (Г, к). The calculations show that the kinetic energy of SCCDP S depends upon the system temperature (1/Г) and it is independent of к for higher screening parameter. The new results of thermal conductivity obtained from an improved HNEMD algorithm are in satisfactory agreement with earlier known numerical results and experimental data for 2D SCCDP S . It is depicted that the HNEMD method is a powerful tool to calculate an accurate plasma thermal conductivity of 2D SCCDP S .