Rebecca Lullo at the Council for Hemispheric Affairs has what I think is a solid take on the future of Iranian-Latin American relations.
Rouhani’s election will likely cause Iranian-Latin American relations to again change course, as he appears more interested in increasing constructive engagement with Washington than further solidifying Iran’s alliances with the United States’ southern neighbors.
In short, dealing effectively with the United States is more important to Iran than deepening ties in Latin America, which of course the U.S. government is sensitive about. Hassan Rouhani would have to make a concerted effort to make the same personal connections that Mahmoud Ahmadinejad, and at this point it's not likely he will. On the other hand, if the U.S. pushes him away, then like Ahmadinejad he will have reason to find allies.
And here is an interesting tidbit I didn't know.
Symbolic of the changing nature of Iran’s relationship with the hemisphere, no Latin American head of state attended Rouhani’s inauguration, even though all were invited by the Iranian government.
Clicking on the link for that bit of news (Radio Free Europe), though, we see that it seems Bolivia and Venezuela will send someone, just not their president:
Iranian allies Belarus, Venezuela, and Bolivia have yet to announce whom they will send.
But did any Latin American head of state attend one of Ahmadinejad's inaugurations? I remember that he came to various ALBA inaugurations, not the other way around. So this isn't necessarily a sign of change. But the overall logic makes sense.
Nonetheless, we are seeing more pressure to identify Iran as a major threat in Latin America, so even if Rouhani pulls back to some degree, expect lots of hot air.