Increasing the frequency and duration of extreme heat events significantly compromises asphalt pavement performance, particularly in critical urban infrastructure such as heavily trafficked pavements, BRT lanes, and intersections subjected to slow-moving heavy traffic under extreme temperatures. This study systematically investigates rutting formation mechanisms through integrated theoretical and numerical approaches, addressing significant knowledge gaps regarding rutting evolution under coupled extreme-temperature (70 °C), heavy-load (100 kN–225 kN), and braking conditions (1 m/s²–7 m/s²). A three-dimensional thermo-mechanical finite element model integrating solar radiation heat transfer with the Bailey–Norton creep law was developed to quantify synergistic effects of axle loads, travel speeds, and braking accelerations. Results demonstrate that when the pavement surface temperature rises from 34 °C to 70 °C, the rutting depth is increased by 4.83 times. When the axle load is increased from 100 kN to 225 kN, the rutting of conventional asphalt pavements under 70 °C is increased by 56.4%. Rutting is exacerbated by braking acceleration; due to prolonged loading duration under low acceleration, the rutting depth is increased by 30–40% compared with that under emergency braking. These findings establish theoretical foundations for optimizing pavement design and material selection in slow-moving heavy-load environments, delivering significant engineering value for transportation infrastructure.