After the second world war, the allies set up temporary governments in several countries. The goal was to let these countries be governed by whom?

Europe had been utterly devastated by World War II. In much of the continent formerly occupied by the Germans, there were no fully-functioning governments, and so the Allied powers stepped in to provide military administrations that would govern the newly-liberated countries until they could get back on their feet.
The United States and Great Britain were concerned that anarchy would break out if they didn't provide some kind of temporary government. It was feared that such conditions would provide an ideal breeding-ground for Communism, especially in a country like Italy, which had a large, well-organized Communist party with mass popular appeal.
In the short-term, then, the Allied plan was for temporary military administration. But in the long-term, it was hoped that the countries of Continental Europe would be able to govern themselves again, once any existing territorial disputes had been resolved.