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Radiocarbon observations suggest that the deep Atlantic Ocean takes up to several centuries to fully respond to changes at the sea surface. Thus, the ocean's memory is longer than the modern instrumental period of oceanography, and the determination of modern warming of the subsurface Atlantic requires information from paleoceanographic data sets. In particular, paleoceanographic proxy data compiled by the Ocean2k project indicate that there was a global cooling from the Medieval Warm Period to the Little Ice Age over the years 900-1800, followed by modern warming that began around 1850. An ocean simulation that is forced by a combined instrumental proxy reconstruction of surface temperatures over the last 2,000 years shows that the deep Atlantic continues to cool even after the surface starts warming. As a consequence of the multicentury surface climate history, the ocean simulation suggests that the deep Atlantic doesn't take up as much heat during the modern warming era as the case where the ocean was in equilibrium at 1750. Both historical hydrographic observations and proxy records of the subsurface Atlantic are needed to determine whether the effects of the Little Ice Age did indeed persist well after the surface climate had already shifted to warmer conditions.