Why is it believed that a Muslim will eventually get out of hell?

To best of my knowledge, according to the most common interpretation, if a person is assigned to hell in the afterlife, he will stay there forever except if he's a Muslim. It's believed that, a Muslim will eventually get out of hell, and go to heaven after paying the price for his sins in hell. Where does this belief originate from? What evidences do we have from Quran and hadith that hell is temporary for Muslims, but eternal for all others?