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The future response of the atmospheric circulation to increased anthropogenic forcing is uncertain, in particular due to competing influences of the large projected warming at the surface in the Arctic, and at upper-levels in the tropics. In the present study two ensembles of fully-coupled 21st century climate simulations are used to analyze changes in the wintertime eddy-driven jet in the North Atlantic and the relation to the well-defined thermal signatures of climate change. The models project a robust reinforcement of the eddy-driven jet and a decrease in waviness and blockings, that we attribute to a narrowing of the westerly flow in mid-latitudes. Composite analyses suggest that this signal is driven by the opposite influence of Arctic and tropical warming on each flank of the jet. We find that a significant portion of the multi-model spread in the jet metrics can be explained by the ratio between these two signals. The tug-of-war between the two effects influences by how much wintertime cold extremes diminish at the end of the 21st century. Models with dominant tropical warming (i.e. narrower and stronger eddy-driven jet) exhibit less decrease in cold extremes with climate change, due to the maintenance of cooler conditions in the subpolar North Atlantic and subarctic seas compared to models with a predominance of Arctic warming.