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Due to the increasing chip temperature and the strong dependency of leakage power on temperature, thermal aware power management has received a considerable amount of attention recently in energy efficient system design. In this paper, we propose a temperature-aware intra-task scheduling algorithm to minimize leakage energy in real-time systems. The basic idea of our algorithm is to run tasks at full speed when the chip temperature is low or the work urgency is high, and switch the processor to a low-power state when the chip temperature is high or the workload is light. Our offline algorithm can achieve the optimal leakage reduction for a given task with the worst-case execution time, while the online algorithm has a very low runtime complexity. The simulation results show that the online algorithm is able to reduce 34% of total leakage energy on average in both real-world and artificial benchmarks. Finally, we demonstrate how to combine our algorithm with existing dynamic voltage scaling technique to optimize the overall energy consumption.