Since a steam iron draws some serious current, I would not mess around with the old plug, but replace it with a new one.
Whatever you could do to the old contacts, they would be prone to oxidize again, probably worse and more quickly than before. And you don't want a high contact resistance for this kind of load: The contacts will run hot, oxidize even more, run even hotter, causing the contatcs in your power outlet to run hot and oxidize as well... creating a real hazard.
It is also possible that the contacts have run hot because of a bad connection between the plug contacts and the cable; replacing the plug will fix that as well. Please be sure to make a proper connection there, using crimped end sleeves on the wires!
The discoloring of the contacts which you describe suggests that they have already run quite hot. It would be a good idea to also check (and possibly replace) the power outlet which you use for the iron. Depending on how comfortable you feel around mains power, and what your local regulations are, this might be a job for a licensed electrician though.