From the perspective of the United States State Department, yes the Cold War would eventually end, but no it was not going to end in the twentieth century. When the State Department drafted vision statements for various Eastern European nations, for example, they always assumed that at least some of these nations would join the European Economic Community (the precursor to the European Union) after the Cold War ended. They were right about that. They were very wrong in predicting when the Cold War would end, however, as even in the 1980s during the period of Perestroika and Glasnost ("restructuring" and "openness" in Russian, i.e., the period of Soviet reform under Gorbachev), the State Department continued to assume that the Cold War would continue for decades. As all historians of the period are aware, so too did the political scientists of the time.

This is obviously just one perspective (the American diplomatic perspective), and I am still interested what others will have to say about this topic.