Fast thermal simulation for System on Chip (SoC) plays a crucial role in integrated circuit (IC) design industry, particularly as power density escalates with increasing computational requirements. It is imperative to assess thermal performance comprehensively during the design phase, utilizing a rapid and precise thermal simulator to expedite design iterations. In this paper, we introduce a fast, physics-aware thermal simulator that draws inspiration from Fourier's law and the Fourier-Biot equation, which correspond to the first and second derivatives of the temperature map. Consequently, the learning objective evolves from merely translating images to approximating natural phenomena such as the thermal gradient and thermal laplacian. By replacing the image-based loss with thermal-aware loss, the proposed model achieves lower prediction error, higher data efficiency, and more physically accurate behavior. The present model demonstrates a significant improvement, achieving a 34% reduction in Maximum Temperature Error (MTE), showcasing the potential for integrating physics-aware learning into SoC thermal design.