There is no phrase in Japanese directly corresponding to "thank you in advance".
I often say よろしくお願いします at the end of the message.
I think よろしくお願いします and "thank you in advance" share the same __function__.
I say and write よろしくお願いします in business or other occasions millions of times at the end of conversations, phones, and mails. This is the most useful Japanese phrase to me.