Earth is the only habitable planet in the solar system and beyond in interstellar space for a distance that would take us at least 80,000 years to traverse at the speed of Voyager 1. Thus our home planet is “This Island Earth”. Here we use our Simple (engineering-type) Climate Model to calculate the change in global-mean near-surface air temperature from 1765 through the third millennium for historical emissions and two scenarios of future emissions of greenhouse gases: (1) a Reference scenario of unabated emissions, and (2) our Fair Plan scenario wherein emissions are phased out to zero from 2020 to 2100. The temperature change for the Reference cases increases to 5.2^°C (9.4^°F) in 2225 and remains there for at least 40 human generations. By design, the temperature change for the Fair Plan increases only to 2^°C (3.6^°F)—the limit adopted by the UN Framework Convention on Climate Change “to prevent dangerous anthropogenic interference with the climate system”—in 2082 and thereafter decreases through the remainder of the millennium. Accordingly, we need to adopt the Fair Plan to safeguard the climate of “This Island Earth”.