Adopt the habit of sending a thank you to all the people who help you along your way, from those who provide initial contacts, offer sage advice or make company recommendations to those who formally interview you.
While the content, tone and format might vary, the end goal of keeping the letter clear and focused should not. And while you might include a sentence or two that reinforces the idea that your background would fit well and be of benefit to the company, don't lose sight of your overall purpose: to thank the recipient for the help they've provided you.
Thank you notes need not be hard copy sent through the mail, but they should be written. A voice mail message just won't have the same effect. And while it's not necessary that a thank you be sent immediately following your conversation or interaction, the sooner you can send it, the better. If too much time passes, the recipient will only have a harder time remembering you and what you spoke about. Strike while the iron is hot!
Generally speaking, if all your interaction with the recipient up until this point has been via email, an email thank you will probably be sufficient. When in doubt, send a letter via mail. Either way, make sure to include a line indicating that you "hope they won't mind if you periodically stay in touch," as this can provide a means for you to go back to them with further questions or for more information.