Overheating has been acknowledged as a major problem during the testing of complex system-on-chip integrated circuits. Several power-constrained test-scheduling solutions have been recently proposed to tackle this problem during system integration. However, we show that these approaches cannot guarantee hot-spot-free test schedules because they do not take into account the nonuniform distribution of heat dissipation across the die and the physical adjacency of simultaneously active cores. This paper proposes a new test-scheduling approach that is able to produce short test schedules and guarantee thermal safety at the same time. Two thermal-safe test-scheduling algorithms are proposed. The first algorithm computes an exact (shortest) test schedule that is guaranteed to satisfy a given maximum temperature constraint. The second algorithm is a heuristic intended for complex systems with a large number of embedded cores, for which the exact thermal-safe test-scheduling algorithm may not be feasible. Based on a low-complexity test-session thermal-cost model, this algorithm produces near-optimal length test schedules with significantly less computational effort compared to the optimal algorithm