Tuning thermal conductivity of porous graphenes has attracted much interest in the thermal management of nanoelectronics devices due to the promising multifunctional properties of engineered nanomaterials. To explore the potential of tuning thermal properties of monolayer porous graphenes in multiple scales, non-equilibrium molecular dynamics (NEMD) and finite element method (FEM) are implemented to manipulate their thermal conductivity and temperature distribution by the engineering of pore topology. Results indicate that the thermal conductivity of porous graphenes can be significantly lower than a pristine graphene. The thermal conductivity reduction is attributed to phonon scattering at the boundaries of defects described by the phonon density of states analysis. It is found that the thermal conductivity and the temperature distribution of a porous graphene can be desirably tuned by the simultaneous engineering of relative density, pore topology, and pore orientation. Then, the effect of unit cell periodicity on the thermal conductivity of periodic porous graphenes, called phononic graphene or graphene metamaterial, is explored. Finally, comparing the results of continuum mechanics approach through the implementation of FEM and NEMD simulation presents the advantages of NEMD for predicting the thermal conductivity of engineered porous graphenes with characteristic length of lower than 50 nm. (C) 2018 Elsevier Ltd. All rights reserved.