A multitude of biogeochemical feedback mechanisms govern the climate sensitivity of Earth in response to radiation balance perturbations. One feedback mechanism, which remained missing from most current Earth System Models applied to predict future climate change in IPCC AR6, is the impact of higher temperatures on the emissions of biogenic volatile organic compounds (BVOCs), and their subsequent effects on the hydroxyl radical (OH) concentrations. OH, in turn, is the main sink term for many gaseous compounds including methane, which is the second most important human-influenced greenhouse gas in terms of climate forcing. In this study, we investigate the impact of this feedback mechanism by applying two models, a one-dimensional chemistry-transport model, and a global chemistry-transport model. The results indicate that in a 6 K temperature increase scenario, the BVOC-OH-CH4 feedback increases the lifetime of methane by 11.4% locally over the boreal region when the temperature rise only affects chemical reaction rates, and not both, chemistry and BVOC emissions. This would lead to a local increase in radiative forcing through methane (Delta RFCH4) of approximately 0.013 Wm(-2) per year, which is 2.1% of the current Delta RFCH4. In the whole Northern hemisphere, we predict an increase in the concentration of methane by 0.024% per year comparing simulations with temperature increase only in the chemistry or temperature increase in chemistry and BVOC emissions. This equals approximately 7% of the annual growth rate of methane during the years 2008-2017 (6.6 +/- 0.3 ppb yr-1) and leads to an Delta RFCH4 of 1.9 mWm(-2) per year.