The role of nanodielectrics in the electrical power system is becoming crucial owing to its superior properties and potential applications in the field. Yet, the materials face limited breakdown strength and thermal properties. Further, the nanodielectrics have not found a comprehensive commercial platform because of the costly manufacturing process, and characterization and testing facilities. Therefore, to reduce the involved cost, in this work, an FE (finite element) based computational technique has been implemented to visualize the effect of shape, size, and filler concentration under the application of high voltage (HV). The epoxy-based nanodielectrics have been modeled incorporating a range of different shapes and size nanofillers—Al2O3, BN, BeO, SiO2, and TiO2. The paper discusses the 2D-analysis of the modeled nanodielectric in the steady-state electrostatic fields and thermal domains. It shows the insights of the nanofillers’ choice to ensure a perfect blend of electrical and thermal properties. The epoxy with square-shaped BeO fillers showed a rise in the electric field of nearly 1.5 times than unfilled neat epoxy, which indicates a significant surge in thermal conductivity at specific filler loading.