Graphene-based nano structures are recently proposed to function as additives to improve the conductivity of thermally sluggish phase change materials (PCMs). Based on existing researches, the improvement is dependent not only on the matrix material, but also on the geometry of the carbon structure. To gain more insight into the nano-scale thermal transport problem, we launch the current pilot research using water as the matrix material, to represent the hydroxyl-grouprich sugar alcohols as PCMs. We have found that the heat conduction across a graphene layer to water is much faster than the heat conduction to the graphene layer itself. Also, the high graphene-water thermal contact resistance fails to acknowledge the fast thermal kinetics of the low frequency phonons. In the investigation of the geometry effect, the cross-plane heat transfer coefficient is found to decrease with decreasing CNT diameter with an exception of the CNT(9,9).