The chemical sink of atmospheric methane (CH₄) depends on the temperature and on the chemical composition. Here, we assess the feedback on atmospheric CH₄ induced by changes in the chemical sink in a warming climate using a CH₄-emission-flux-driven set-up of the chemistry-climate model EMAC (ECHAM/MESSy Atmospheric Chemistry), in which the chemical feedback of CH₄ mixing ratios can evolve explicitly. We perform idealized perturbation simulations driven either by increased carbon dioxide (CO₂) mixing ratios or by increased CH₄ emission fluxes. The CH₄ emission flux perturbation leads to a large increase of CH₄ mixing ratios. Remarkably, the factor by which the CH₄ mixing ratio increases is larger than the increase factor of the emission flux, because the atmospheric lifetime of CH₄ is extended. In contrast, the individual effect of the global surface air temperature (GSAT) increase is to shorten the CH₄ lifetime, which results in a significant reduction of CH₄ mixing ratios in our set-up. The corresponding radiative feedback is estimated at -0.041 and -0.089 W m^-2 K^-1 for the CO₂ and CH₄ perturbation, respectively. The explicit response of CH₄ mixing ratios leads to secondary feedbacks on the hydroxyl radical (OH) and ozone (O₃). Firstly, the OH response includes the CH₄-OH feedback, which enhances the CH₄ lifetime change, and, secondly, the formation of tropospheric O₃ is reduced.