how does the temperature of the earth change, when the sun suddenly stop radiating?

Answer 1

If the Sun were to suddenly vanish at this very moment, the light from the Sun would continue to arrive for the next 8.5 minutes which is the travel time from the Sun to the Earth at the speed of light. There would still be a Sun in the sky even though the Sun is actually not there now. So far as we know, and so far as the little data we have can tell us, gravity and the force of gravity also travels at the speed of light. This means the Sun's gravitational force takes 8.5 minutes to cross the solar system to get to the Earth and affect the orbit of the Earth. If the Sun were to vanish, the gravitational force that it emitted before vanishing would still be on its way and would not stop coming for 8.5 minutes after the Sun had been removed

Then we would have serious problems. Certainly within a week the temperature on Earth would have dropped below freezing. People on the coasts might survive longer than the rest, because of the heat the oceans would release; on the other hand I could imagine some intense weather along the coasts due to the temperature gradients. People with large energy reserves would also last longer. I suppose the place to be would be in the ocean, under the layer of insulating ice that would form, near a geothermal vent (not recommended if you breathe air) -- I'm not sure how long life here could last.

Answer 2

All life would end by the time the oceans froze solid in a few thousand years, except for bacteria in hydrothermal vents on the ocean floor. The vents supply heat and food, and such bacteria do not need oxygen.

Answer 3

we would all be VERY cold. Imagine being under a sun lamp and that going off.