The anisotropic heat transport in graphene–CNT based materials provoked the development of three-dimensional pillared-graphene (PG) systems. In this study, we performed non-equilibrium molecular dynamics simulations to analyze PG thermal conductivity and thermal boundary conductance. For the first time, we have considered the influence of pillar chirality and the temperature effect on PG heat transport. We analyzed the influence of pillar chirality and pillar length on the in- and out-of-plane transport properties. For the temperature-dependent analysis, the chosen temperatures were in the range of 100 K to 500 K. To elucidate the mechanism underlying the heat transport, we investigated the phonon density of states (DOS) in the different regions of PG systems. The overlap factor was calculated to quantify the mismatch in the phonon DOS profiles. Across the pillar region, the overlap factor correlates directly with the thermal boundary conductance. When heat is transported in an out-of-plane direction, the zig-zag PG system performs better than the armchair PG system. The atomic arrangement at the graphene–CNT interface plays an inevitable role in limiting heat transport in PG systems. The calculated phonon energy in the zig-zag PG interface is higher than that in the armchair PG interface.