And here is a serious paper (fee required for more than an abstract) called "The catastrophic extinction of North American mammoths and mastodonts" by Gary Haynes, which will explain in detail why it was humans, not climate, that did in the elaphants.
Thanks to Reid for the paper versions.
Cast of mastodon tooth by paleoarchaeologist Laura Niven. Notice the breast-like shape of the cusps -- 'mastodont' = 'breast-tooth.' The teeth of elephants and mammoths have fine parallel ridges instead.