It's been done.

Paul Rogat Loeb has an idea: A videogame version of An Inconvenient Truth.

Given that we need to reach more people, how about an Inconvenient Video Game, a Sim World where players learn about the issues surrounding global warming, choose paths of action to address it, and link to real-world external websites? The goal would be to navigate America (and help navigate the planet) through what it will take to emerge without disaster. Players could research the facts, make good or bad choices, and see the consequences of various actions taken. The game could even include some modeling of political advocacy, so players could take the role of ordinary citizens, since our efforts will ultimately decide whether America ever does really addresses one of the most complex and urgent crises in human history.

Most of the empire-building games I've played in the last while - and there haven't been many - have made you do exactly that when your civilization gets to big and advanced. Then of course there was SimEarth in the early 1990s, where the objective was to manage the ecosphere properly. The easy thing to do when the CO2 got too high was just turn down the sun. The political utility of that approach is doubtful.