I wrote a letter to my donor family, too. I was not ready to do it until about 4-5 months after my transplant. I waited until I was recovered enough that I felt the physical and the emotional strength to put pen to paper.
For me it was extremely difficult to do. Like you, I was grieving for a family that I didn't know. But at the same time, I knew my donor in a most intimate way because now he/she is a living part of me. Many people think I am crazy and tell me that I shouldn't to feel that way. (I wonder if anyone else feels this way?)
There are no words that exist to say I'm sorry and thank you at the same time. I plodded through and after many rewrites, I came up with a letter that was satisfactory to me. I didn't even mail it right away, but waited a few days to be sure that it was just right to express my feelings. I felt a real sense of peace when I finally put the envelope in the mail box.
A few months later, I got a call from my transplant department and was asked if I would like them to forward a letter from my donor family to me. I never expected that to happen! But I secretly hoped that it might because maybe it would give me some closure to the guilt that I felt. When the mail man handed the letter to me, I had to sit down and to hold it for a few minutes before I was ready to open it. My hands were shaking and my tears were dripping on the envelope.
In that letter, I learned that my handwritten note, containing my condolences and my thanks, was well received. My donor family expressed appreciation that I contacted them. They told me a little about my donor. And then told me that they wanted me to enjoy my life. Which I do!
I did send a note on once as an update, but that is the end of any correspondence.