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We have investigated spin transfer torque random access memory (STT-RAM) with a thermal-assist programming scheme using finite-element thermal simulation. We conducted the study on a specific memory element design to analyze the thermal dynamics and thermal programming mechanism. We paid particular attention to the scalability and design potential of the thermal-assist programming scheme by varying the memory element dimension and resistance-area product. In addition we systematically analyzed and compared thermal-assisted STT-RAM and standard STT-RAM based on these results. Finally, we provide a summary of the programming scheme and some recommendations for improving writeability and scalability of this technology.