With the increase of the number of cores in computers, temperature-aware multi-core task scheduling algorithms have become a research hotspot in computer systems. In recent years, machine learning has shown great potential in various fields, and thus many work using machine learning techniques to manage system temperature have emerged. Among them, reinforcement learning is widely used for temperature-aware task scheduling algorithms due to its strong adaptability. However, the state-of-the-art temperature-aware task scheduling algorithms based on reinforcement learning do not effectively model the system, and it is difficult to achieve a better trade-off among temperature, performance, and complexity. Therefore, this study proposes a new multi-core temperature-aware scheduling algorithm based on reinforcement learning-ReLeTA. In the new algorithm, a more comprehensive state modeling method and a more effective reward function are proposed to help the system further reduce the temperature. Experiments are conducted on three different real computer platforms. The experimental results show the effectiveness and scalability of the proposed method. Compared with existing methods, ReLeTA can control the system temperature better.