The Network-on-Chip (NoC) interconnection is a popular way to build up contemporary large-scale multi-processor System-on-Chip (MPSoC) systems. However, due to the high integration density with high operation frequency, the larger power density leads to serious temperature problems. The thermal issue limits the performance and results in higher leakage power and lower system reliability. The thermal and power issues become worsen in the modern 3D stacking NoC structure and become the primary design challenge. In this chapter, we first investigate the correlation between power and temperature in NoC systems and introduce a thermal model for such systems. With this thermal model, we introduce novel routing design methodologies for power- and temperature-aware NoCs by using Game theory and reinforcement learning.