The high-temperature and high-humidity conditions arising from the biochemical degradation of landfill waste result in significant temperature gradients within the landfill cover. The effects of waste temperature on landfill gas transport and microbial aerobic methane oxidation are not fully understood. In this study, a fully coupled theoretical model was developed to simulate the interactions of moisture, heat, and gas transport within a capillary barrier cover. A series of parametric studies were carried out to investigate the influence of the combined effects of temperature gradient, initial soil moisture content, and landfill gas generation rate on methane transport, oxidation, and emissions. The simulated results indicated that increasing waste temperature intensified the temperature gradient, leading to higher surface evaporation rates and variations in methane oxidation efficiencies. Additionally, variations in initial soil moisture content and landfill gas generation rates were found to significantly impact gas migration and methane oxidation in the cover. This study demonstrates the critical role of waste temperature in landfill gas migration within landfill cover systems, providing technical methodologies for the optimized design of soil cover systems.