Methane emissions through landfill cover is a complicated multi-physics coupled process, including water-gas-heat transfer and microbial aerobic methane oxidation (MAMO). Due to the relatively high water content of municipal wastes in China, landfill gas generally contains a substantial amount of water vapor. Moreover, the biochemical decomposition of wastes underneath landfill cover results in noticeable temperature gradient across the cover. Nevertheless, effects of water vapor and temperature gradient on water and gas distributions in landfill cover are not clear. A new theoretical model of water-gas-heat reactive transfer and MAMO in unsaturated soils was developed by incorporating vapor flow and effects of temperature gradient on water and gas transfer. The newly proposed model was implemented in a finite-element software COMSOL. The model was verified by (i) a published soil column test simulating MAMO; and (ii) a soil column test subject to heating. The model is capable of describing liquid water-vapor transfer, multi-component gas transfer (e.g., CH4, CO2, N2 and O2), heat transfer and MAMO. The theoretical model and the related numerical code could serve as a useful tool for landfill cover design for mitigating methane emissions.