Why did Alexander the Great build temples in conquered lands?

Because he believed that the only way of creating prosperous Empire is by strengthening the culture and honoring the religious diversity of his country. He wanted to blend Greek culture with the Eastern cultures and that is why he built roads, temples, even cities.

Explanation:

Although Alexander The Great is mostly known as a great conqueror, he is also important because during his reign a new form of culture emerged, known to us as Hellenism. During that period many important artists, philosophers, historians, etc. were spreading the ideas of Alexander. It was something never seen until then. They respected each others and their diversity.