My thesis director was a head of department for 10 years, then Principal of a college for another 10. We still have dinner every month or two. He has helped me through many, many such letters -- he received them by the thousands every year.
Here is what I know: it should be 2 full pages, and should show you know the "Dr." you're writing to: what his/her research is in, how that relates (in detail) to what you have been working on (in detail); you should also show you know other people at his department, and what they do, and what interests you in their work. Plus, no one wants to read your thesis just yet, don't mail it!
The letter you have written, as is, would immediately be put into the "no" pile. A very large pile.
Really.