Pillared-graphene structure (PGS) is a novel three-dimensional structure consists of parallel graphene sheets that are separated by carbon nanotube (CNT) pillars that is proposed for efficient thermal management of electronics. For microscale simulations, finite element analyses were carried out by imposing a heat flux on several PGS configurations using a Gaussian pulse. The temperature gradient and distribution in the structures was evaluated to determine the optimum design for heat transfer. The microscale simulations also included conducting a mesh-independent study to determine the optimal mesh element size and shape. For nanoscale simulations, Scienomics MAPS software (Materials And Processes Simulator) along with LAMMPS (Large-scale Atomic/ Molecular Massively Parallel Simulator) were used to calculate the thermal conductivity of different configurations and sizes of PGS. The first part of this research included investigating PGS when purely made of carbon atoms using non-equilibrium molecular dynamics (NEMD). The second part included investigating the structure when supported by a copper foil (or substrate); mimicking production of PGS on copper. The micro- and nano-scale simulations show that PGS has a great potential to manage heat in micro and nanoelectronics. The fact that PGS is highly tunable makes it a great candidate for thermal management applications. The simulations were successfully conducted and the thermal behavior of PGS at the nanoscale was characterized while accounting for phonon scattering the graphene/CNT junction as well as when PGS is supported by a copper substrate.