Temperature affects not only the performance but also the power, reliability, and cost of the embedded system. This paper proposes a temperature-aware task allocation and scheduling algorithm for MPSoC embedded systems. Thermal-aware heuristics are developed, and a temperature-aware floorplanning tool is used to reduce the peak temperature and achieve a thermally even distribution while meeting real time constraints. The paper investigates both power-aware and thermal-aware approaches to the task allocation and scheduling. The experimental results show that the thermal-aware approach outperforms the power-aware schemes in terms of maximal and average temperature reductions. To the best of our knowledge, this is the first MPSoC task allocation and scheduling algorithm that takes temperature into consideration.