AGH, no!
My apologies, gibber71, but justadude, don't do that. Don't thank her for making you realize that you're the better person. You certainly are, no doubt about it, and you <i>should</i> realize it, but don't tell her that. You don't know how many women in your area that she might know. Bad reps spread quick in the female subspace network.
Take the breakup gracefully. When she realizes her mistake and comes to you with it (and she just might), go ahead and rub it in her face, but be subtle about it. "Well, I appreciate the apology, but fact is, I was over you the moment you cheated on me. I'm sorry, but you know it's over between us just as well as I do. Please stop calling me." Something like that.
Otherwise, I agree with gibber.