Theoretically, in an informed democracy, the people would recognize the threat and act to stop it by voting in representatives who are committed to curtailing climate change. In the real world, though, our democracy is not that informed. The mainstream media covers stories that are more sexy. I don't believe there were any climate change questions posed at the presidential debates.
The two possible solutions would be to change the system in such a way to foster an informed democracy. The other, as you mentioned, would be an entirely different government system. I think the former solution is more feasible by passing legislation that makes it harder for fossil fuel companies to have so much influence on representatives. I'm not sure how to fix the news. The reason I don't see a different system of government working is because I don't think any system solves the "individual interest > general welfare" problem. Democracy is pretty much as good as it gets when it comes to the general welfare, other than a smart benevolent dictator... but how long has that ever lasted?