Btw, is it true that Luciano was really such a hot tempered guy? He always seemed to me as the more sophisticated and tolerant one.
Yeah, I think much of that is just creative license. We don't really know a whole lot about Luciano's violent tendencies in his early days. His autobiography neatly elides all of that. Certainly compared to men like Siegel, Buchalter, Anastasia and Genovese he was less violent and more level headed. And no simple hothead could wait for long periods of time to play both Masseria and Maranzano against each other and wind up eliminating them both.
But this is supposed to be the early days, in which he is barely removed from the Lower East Side. I've read different stories about how Luciano met Siegel and Lansky but they all involved Luciano threatening or committing violence.

IIRC Luciano and other biographers did say that Rothstein had a calming and scholarly effect on Luciano, who remember would have only been around 22-23 at the start of Prohibition.