High Efficiency Video Coding (HEVC) provides high efficiency at the cost of increased computational complexity followed by increased power consumption and temperature of current Multi- Processor Systems-on-Chip (MPSoCs). In this paper, we propose a machine learning-based power and thermal management approach that dynamically learns the best encoder configuration and core frequency for each of the several video streams running in an MPSoC, using information from frame compression, quality, performance, total power and temperature. We implement our approach in an enterprise multicore server and compare it against state-of-the-art techniques. Our approach improves video quality and performance by 17% and 11%, respectively, while reducing average temperature by 12%, without degrading compression or increasing power.