The quest for high thermal conductivity materials has lead to nano-composites incorporating macromolecular materials with excellent thermal conductivity, such as carbon nano-tubes and graphene nano-ribbons, in a matrix of poorer thermal conductivity. To minimize the interface thermal resistance the stiff, incorporated materials can be chemically functionalized with various side chains, this however may disrupt the overall thermal conductivity of the fillers. We report here an

efficient theoretical method using normal modes to calculate the thermal conductivity of such systems and show how the participation ratio of these modes can be used to evaluate different choices for functionalization. We use this method to examine how effective different organic chains improve the heat flux through a graphene nano-sheet, also to identify the configuration of the functional groups that best conduct heat to the macromolecule. To confirm the efficiency of our

model, we compare results from simulations including non-linear corrections to results from the normal mode analysis conducted on identical systems. Finally, we investigate the effect of space correlated noise on the overall results of optimization.