The postscript at the end of the movie left out a very significant detail! The 52 hostages were released after 444 days of captivity----within minutes after REAGAN was elected POTUS. Reagan left no doubt to the world that the hostage would be released immediately or IRAN would be wiped off the earth asap. He won his "bluff"(?).
You'll find very few serious scholars who think that they released them solely because of Reagan. This is all part of the mythologicization of Reagan that's occurred in the past decade.
The release of the hostages happened after months of negotiation and efforts from the Carter administration. Reagan's inauguration was incidental.