A thermally aware design automation suite integrates system-level thermal awareness into design of semiconductor chips, performing fine-grain static and/or transient thermal simulations of the chips based on thermal models and boundary conditions. The thermal simulations are performed in accordance with one or more grids, with boundaries and/or resolutions being determined by adaptive and/or hierarchical multi-dimensional techniques. The adaptive grid techniques include material-boundary, rate-of-change, and convergence-information heuristics. For example, a finer grid is used in a region having higher temperature gradients compared to a region having lower temperature gradients. The hierarchical grid techniques are based on critical, intermediate, and boundary regions specified manually or automatically, each region having a respective grid resolution. For example, a critical region is analyzed according to a grid that is finer than a grid of an intermediate region, and resolution of a grid of a boundary region is adapted to boundary conditions.