How do you write a letter to one's father's birth father?

My father was adopted through a closed adoption. We had his mother's name, but nothing more. We contacted his mother and discovered that he was conceived out of wedlock. She gave us the name of his birth father and a little further information about him, but nothing further. Since then I have found someone who I am fairly confident is the right man (the same name and a reasonable age, along with living in the same city my father's birth mother mentioned the conception being in), but I am currently a little bit unsure about a number of things: one, whether this is the right man; and two, if this is the right man, if he knows that he has a son by this woman. However, I wish to get in touch with him so that I can have more information on my medical history and so that I can confirm that I've got the right group of people in the family tree I've been working on for two years. I'm not even going to try to call him, because I think I would get a bit too nervous, but I wish to write him a letter. However, I have no idea what to ask and what to say. Any help would be much appreciated.