In this paper we propose an analytical technique for the steady-state dynamic temperature analysis (SSDTA) of multiprocessor systems with periodic applications. The approach is accurate and, moreover, fast, such that it can be included inside an optimization loop for embedded system design. Using the proposed solution, a temperature-aware reliability optimization, based on the thermal cycling failure mechanism, is presented. The experimental results confirm the quality and speed of our SSDTA technique, compared to the state of the art. They also show that the lifetime of an embedded system can significantly be improved, without sacrificing its energy efficiency, by taking into consideration, during the design stage, the steady-state dynamic temperature profile of the system.