The Atlantic cold tongue, which typically peaks in boreal summer, exerts a pronounced regional and global impact on the climate and socio-economy. Projected future changes in the Atlantic cold tongue are full of uncertainty, mainly arising from a model bias in simulating its mean state, with less biased models projecting a stronger weakening in amplitude. However, the underlying mechanisms remain unknown. Here, we find that model bias exerts its influence through modulating atmospheric thermal damping and upwelling of subsurface anomalous warming induced by the weakened Atlantic meridional overturning circulation (AMOC). In less biased models, the Atlantic cold tongue, compared to the western equatorial Atlantic, features a cooler mean climate sea surface temperature (SST), and is subjected to smaller thermal damping induced by mean climate evaporation and consequently, faster SST warming. Moreover, equatorial subsurface warming associated with a reduced AMOC is advected to the surface via mean climate upwelling, enhancing faster SST warming in the east, a feedback stronger in less biased models that produce greater climatological upwelling. The above asymmetric SST warming would be amplified by the Bjerknes feedback, leading to a weakened Atlantic cold tongue. These findings may help to predict future changes in the Atlantic cold tongue and its influences.