Dear ........
You interviewed me on (date) for the (role) position.
I really want this job, so I'm taking the liberty of re-stating why I think you should choose me:
(then list 3-5 short points which relate your skills, knowledge, experience, achievements, character, attitude, to the results and effects they'll be seeking from the person appointed. It is very important that these points demonstrate that you have clearly understood and can deliver - specific measurable things if possible - what they need for the role, for example:)
You might have seen better qualified applicants, or people with more relevant experience, but when it comes down to it, it's the person with the most passion and determination who is able to make a real difference. I'd urge you to give me the chance to prove I am that person.
Yours etc.