The Last Interglacial (LIG), a warmer period 130,000–116,000 years before present, is a potential analogue for future climate change. Stronger LIG summertime insolation at high northern latitudes drove Arctic land summer temperatures 4–5 °C higher than in the pre-industrial era. Climate model simulations have previously failed to capture these elevated temperatures, possibly because they were unable to correctly capture LIG sea-ice changes. Here, we show that the latest version of the fully coupled UK Hadley Center climate model (HadGEM3) simulates a more accurate Arctic LIG climate, including elevated temperatures. Improved model physics, including a sophisticated sea-ice melt-pond scheme, result in a complete simulated loss of Arctic sea ice in summer during the LIG, which has yet to be simulated in past generations of models. This ice-free Arctic yields a compelling solution to the long-standing puzzle of what drove LIG Arctic warmth and supports a fast retreat of future Arctic summer sea ice.