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As technology process node scales down, on-chip SRAM caches lose their efficiency because of their low scalability, high leakage power, and increasing rate of soft errors. Among emerging memory technologies, Spin-Transfer Torque Magnetic RAM (STT-MRAM) is known as the most promising replacement for SRAM-based cache memories. The main advantages of STT-MRAM are its non-volatility, near-zero leakage power, higher density, soft-error immunity, and higher scalability. Despite these advantages, the high error rate in STT-MRAM cells due to retention failure, write failure, and read disturbance threatens the reliability of cache memories built upon STT-MRAM technology. The error rate is significantly increased in higher temperatures, which further affects the reliability of STT-MRAM-based cache memories. The major source of heat generation and temperature increase in STT-MRAM cache memories is write operations, which are managed by cache replacement policy. In this paper, we first analyze the cache behavior in the conventional LRU replacement policy and demonstrate that the majority of consecutive write operations (more than 66%) are committed to adjacent cache blocks. These adjacent write operations cause accumulated heat and increased temperature, which significantly increases the cache error rate. To eliminate heat accumulation and the adjacency of consecutive writes, we propose a cache replacement policy, named Thermal-Aware Least-Recently Written (TA-LRW), to smoothly distribute the generated heat by conducting consecutive write operations in distant cache blocks. TA-LRW guarantees the distance of at least three blocks for each two consecutive write operations in an 8-way associative cache. This distant write scheme reduces the temperature-induced error rate by 94.8%, on average, compared with the conventional LRU policy, which results in 6.9x reduction in cache error rate.