Asphalt bridge deck pavements are highly susceptible to rutting, shoving, and interlayer slippage under high-temperature traffic conditions, where interlayer shear stress plays a decisive role. To clarify the coupled effects of thermal gradients and moving loads, this study developed a sequential three-dimensional thermo-mechanical finite element model for a double-layer pavement in Zhongshan, China. Field-recorded air temperature, solar radiation, sunshine duration, and wind speed were used to define transient thermal boundaries. The calculated temperature field was then transferred to a fully bonded moving-load model with dual rectangular contact areas and braking-induced longitudinal traction. Axle load, roadway slope, braking coefficient, and the thicknesses of the SMA-13 and AC-20 layers were varied. The predicted temperature fluctuation attenuated and the peak time was delayed with depth. The pavement surface reached 58.95 °C at 13:00, whereas the bottom of the asphalt overlay reached 46.99 °C at 17:00. Under the adopted 14:00 near-peak summer condition, increasing axle load amplified the overall response and raised the maximum asphalt-layer shear response from 0.172 to 0.223 Mpa. Roadway slope mainly affected traffic-direction stress transfer. Increasing the braking coefficient from 0 to 0.7 increased longitudinal shear response from 57.9 to 161.2 kPa in the asphalt layers and from 56.4 to 112.6 kPa near the AC-20/concrete interface. Increasing SMA-13 thickness reduced thermal and mechanical demand in the underlying layers, whereas increasing AC-20 thickness reduced the response near the concrete deck but shifted part of the tensile and shear demand toward the upper asphalt layer.