The traditional view is that widespread discharge of freshwater into the North Atlantic leads to a reduction of the Atlantic Meridional Overturning Circulation (AMOC), a concomitant reduction of poleward heat transport and a cooling of the climate of the North Atlantic. Here we report upon coupled atmosphere-ocean general circulation model experiments that suggest a more non-uniform response of the North Atlantic climate to large freshwater perturbations. We show that in a cold climate with extensive sea ice coverage in the Labrador Sea, a massive discharge of freshwater along coastal boundaries leads to an anomalous warming in the western North Atlantic. The warming persist despite a significant weakening of the AMOC and its associated heat transport. It is maintained by major reorganizations of the large-scale wind field, oceanic circulation and convection in the subpolar Atlantic.