In the episode Operation: Annihilate! Kirk finds his brother dead. He didn't seem very upset (definitely no tears, was able to continue with work immediately). Was there any reason in particular for this? Or did the director make the choice because it would have been boring to see his sadness played out for too long?
EDIT: I somewhat disagree with the answers given. Kirk does show emotion, including negative ones. For example in the episode Miri he gets mad when they weren't finding a cure to the disease fast enough and smashes some flasks, and this episode happens prior to "Operation: Annihilate!".