Nige,
Interesting question. Your resting heart rate of 38 is definitely below what is considered normal (60-100). However, physical fitness can definitely affect this. I have seen professional basketball players who routinely have resting rates in the 30's.
The question to be answered: is this low rate OK for you?
You will need to consult with your physician who will take a history and examine you. He will then decide if further evaluation is necessary. By your letter, your heart rate does respond to exercise as expected. The need for a stress test will be determined by your physician. Your father's history is also a factor in his decision process.
Thanks again,
Martin Cane, M.D.