And the LA Times explains how they do it.

As the film business has become an increasingly global one, Dempsey’s job has become ever more complex, with languages in emerging territories added every year. The newest additions include Bengali, Malay and Vietnamese. While “Frozen” is available in 41 languages, Dempsey recalls casting for about 15 languages on “The Lion King” in 1994….For Dempsey, “Frozen’s” music posed a special challenge: He had to mimic the vocal tone and texture of Menzel, a Tony Award-winning soprano famous for her penetrating pipes. “Idina has one of the best voices, period, in terms of her smooth tone, the warmth when she hits the lower end,” Dempsey said. “In certain territories — Taiwan, Cantonese — the voice might want to be thin because that’s part of the culture. It was always a challenge to find her match.”