During recent decades, there has been dramatic Arctic sea ice retreat. This has reduced the top-of-atmosphere albedo, adding more solar energy to the climate system. There is substantial uncertainty regarding how much ice retreat and associated solar heating will occur in the future. This is relevant to future climate projections, including the timescale for reaching global warming stabilization targets. Here we use satellite observations to estimate the amount of solar energy that would be added in the worst-case scenario of a complete disappearance of Arctic sea ice throughout the sunlit part of the year. Assuming constant cloudiness, we calculate a global radiative heating of 0.71 W/m2 relative to the 1979 baseline state. This is equivalent to the effect of one trillion tons of CO2 emissions. These results suggest that the additional heating due to complete Arctic sea ice loss would hasten global warming by an estimated 25 years.