The last glacial cycle provides the opportunity to investigate large changes in the Atlantic Meridional Overturning Circulation (AMOC) beyond the small fluctuations evidenced from direct measurements. Paleotemperature records from Greenland and the North Atlantic show an abrupt variability, called Dansgaard–Oeschger (DO) events, which is associated with abrupt changes of the AMOC. These DO events also have Southern Hemisphere counterparts via the thermal bipolar seesaw, a concept describing the meridional heat transport leading to asynchronous temperature changes between both hemispheres. However, temperature records from the North Atlantic show more pronounced DO cooling events during massive releases of icebergs known as Heinrich (H) events, contrary to ice-core–based temperature records from Greenland. Here, we present high-resolution temperature records from the Iberian Margin and a Bipolar Seesaw Index to discriminate DO cooling events with and without H events. We show that the thermal bipolar seesaw model generates synthetic Southern Hemisphere temperature records that best resemble Antarctic temperature records when using temperature records from the Iberian Margin as inputs. Our data-model comparison emphasizes the role of the thermal bipolar seesaw in the abrupt temperature variability of both hemispheres with a clear enhancement during DO cooling events with H events, implying a relationship that is more complex than a simple flip-flop between two climate states linked to a tipping point threshold.