This paper presents a power-aware adaptive meshing technique. It is suitable for steady-state finite-element (FE) thermal analysis of integrated circuits. Unlike most of the adaptive meshing techniques, the proposed algorithm does not require any iterative solutions. Rather, the proposed algorithm analyzes the layout in one pass to detect critical areas in need for fine meshing. A suitable mesh size is selected for these areas, and the FE analysis is done only once. The algorithm results showed comparable accuracy and better performance when compared to the flux-based adaptive meshing algorithm.