Could I cool down the Earth by capturing a comet and dropping it in the ocean, like an ice cube in a glass of water?
No. In fact, it’s honestly sort of impressive to find a solution that would actively make the problem worse in so many different ways.
Outer space is a lot higher up than Niagara Falls, so the plunge down into the atmosphere at the bottom of Earth’s gravity well adds a lot more than 0.1 degrees worth of heat. A chunk of ice from space that falls to Earth gains enough energy to warm the ice up, melt it, boil it into vapor, and then heat the vapor to thousands of degrees. If you built an icy waterfall from space, the water would arrive at the bottom as a river of superheated steam.Source: What If?
The rest of that post, as always, is amazing. This is what I needed in school (but never had).
And all I wanted to add was: damn, I miss Futurama. One of the best shows.