Wolf et alAbstract:As the Sun slowly grows brighter over its main sequence lifetime, habitability on Earth’s surface will eventually become threatened probably leading to moist and then runaway greenhouse climates. One-dimensional climate models predict that a catastrophic thermal runaway will be triggered by a 6% increase in the solar constant above its present level. However, here simulations using a three-dimensional climate model with fixed carbon dioxide and methane indicate that surface habitability may be maintained at significantly larger solar constants. A 15.5% increase in the solar constant yields global mean surface temperatures of 312.9K, well short of moist and runaway greenhouse states. Numerical limitations prevent simulation of climates much warmer than this. Nonetheless, our results imply that Earth’s climate may remain safe against both water loss and thermal runaway limits for at least an other 1.5 billion years and probably for much longer.