I haven't found any particularly historically accurate podcasts about the Mongols, specifically about the rise and fall of the empire. Wrath of the Khans is good in as much as it is flashy, interesting history. Historically accurate, not so much. We've had lengthy discussions about his body of work on this sub and, from what I understand, the ultimate conclusion is that he is a showman and not a professional historian. Edited to take out a speculative statement

But, the AskHistorians podcast had two episodes about the Mongols which were very good and had discussion threads with them! Episode 024 about the Ilkhanate, discussion thread here and Episode 25 about the Mongol Yuan Dynasty, discussion thread here.

Edit: Took out the statement quoted below. I should not have implied that professional historians are always right. My intention was to articulate that Dan Carlin is factually incorrect sometimes.

Edit 2: In no way am I trying to take anything from the value of Dan Carlin's podcasts. I am trying to convey that he is entertaining, but should not be taken completely as fact. I've talked about Dan Carlin before: On Dan Carlin and Popular History

The thegreatcourses.com has lectures called 'The Barbarian Empires of the Steppes'. Its not only about mongols but if you have liked the Dan Carlin Podcast you will defently like this as well. Its not quite so narratively driven but the Prof is a pleasure to listen. You also get far broader view on topics that Carlin did not really covered.

The Audio is sufficent. Their videos don't add enough to be worth the price. The Audio download price is more then a usual Audiobook but I think its worth the money.

http://www.thegreatcourses.com/courses/the-barbarian-empires-of-the-steppes.html

In Our Time has a good discussion about Genghis and the rise of the Mongols. It's only one episode, but its well worth a listen. http://www.bbc.co.uk/programmes/b00773mr