The abrupt nature of warming events recorded in Greenland ice-cores during the last glacial has generated much debate over their underlying mechanisms. Here, we present joint marine and terrestrial analyses from the Portuguese Margin, showing a succession of cold stadials and warm interstadials over the interval 35-57 ka. Heinrich stadials 4 and 5 contain considerable structure, with a short transitional phase leading to an interval of maximum cooling and aridity, followed by slowly increasing sea-surface temperatures and moisture availability. A climate model experiment reproduces the changes in western Iberia during the final part of Heinrich stadial 4 as a result of the gradual recovery of the Atlantic meridional overturning circulation. What emerges is that Greenland ice-core records do not provide a unique template for warming events, which involved the operation of both fast and slow components of the coupled atmosphere-ocean-sea-ice system, producing adjustments over a range of timescales. Interstadial North Atlantic warming during the last glacial period involved the operation of both fast and slow components of the coupled atmosphere-ocean-sea-ice system, according to analyses from the Portuguese Margin and climate model simulations.