Don't ever thank a girl for going out with you. It makes it look like you are acknowledging that she is too good for you, and thus is doing you a favor by even giving you the time of day.
If you sense that a girl has some degree of interest in you (which she probably does here, since she's willing to go on a second date), the best way to act is "moderately interested".
That is, don't act too excited or too enthralled with her, but also don't act like a hard-to-get, aloof asshole. Show interest in spending time with her and talking to her on the phone, but don't kiss ass or rave about what a great catch she is.
Groucho Marx once said, "I'd never join a club that would have me as a member." Unfortunately, that's the way a lot of people view dating, especially women.