I heard from Rabbi Shlomo Wolbe z"l (circa 1981), that there will never be nuclear extinction.

He explained, that he is not a prophet, but he can still state that with the utmost confidence. 

That is because according to Jewish thought, throughout the generations, there is a constant battle between "good" and "bad". However ultimately, "good" will triumph, and the Messianic era will be ushered in.

The scenario of nuclear extinction, he posited, would mean that "bad" has triumphed, and the Messianic prophecies would never be fulfilled. Theologically, that is impossible.