How long would it take for the Earth to freeze if the Sun burnt out?

Different parts of the Earth would freeze at different rates if the Sun were to suddenly go out. We can guess some of the rates just from considering what happens at night. Over the course of 12 hours without sunlight, temperatures tend to drop between 10 and 30 degrees Fahrenheit, depending on whether you're in a desert or near the ocean. So you might expect that things would start to freeze in only two or three days with no sun.

The ocean acts like a big reservoir of heat, since its layers can mix and bring warm material easily to the surface. Areas near the ocean would remain warmer for a while longer, but the freezing would probably start in only a few months. After the time of an arctic winter, the ocean would be filled with pack ice. Since the pack ice of the arctic ocean averages about a dozen feet thick during the winter, one might guess the oceans would freeze at about the rate of a 50 feet a year. This rate would slow as a thick blanket of insulating ice was accumulated, but the effect would be the same, the warm water would be so far down as to be useless to people on the surface unlucky enough to be looking for it. Eventually, the atmosphere would liquefy and then freeze. That would probably take a few decades to begin.

We don't expect the Sun to shut off anytime within the next five billion years, but the same effects would occur if a lot of dust blocks light from reaching the surface of our planet. This happened on a big scale 60 million years ago when an asteroid hit our world. The resulting ice age killed the dinosaurs (and many other plants and animals). On a smaller scale, volcanoes affect weather every few years.