The climate of the last glacial period was extremely variable, characterized by abrupt warming events in the Northern Hemisphere, accompanied by slower temperature changes in Antarctica and variations of global sea level. It is generally accepted that this millennial-scale climate variability was caused by abrupt changes in the ocean thermohaline circulation. Here we use a coupled ocean-atmosphere-sea ice model to show that freshwater discharge into the North Atlantic Ocean, in addition to a reduction of the thermohaline circulation, has a direct effect on Southern Ocean temperature. The related anomalous oceanic southward heat transport arises from a zonal density gradient in the subtropical North Atlantic caused by a fast wave-adjustment process. We present an extended and quantitative bipolar seesaw concept that explains the timing and amplitude of Greenland and Antarctic temperature changes, the slow changes in Antarctic temperature and its similarity to sea level, as well as a possible time lag of sea level with respect to Antarctic temperature during Marine Isotope Stage 3.