Aside from people mentioning that they do indeed have emotions, I also want to point out an accurate portrayal of a being with no emotions at all would be a boring being that doesn't do anything at all. With no emotion we have no reason to do anything, we don't want anything, we wouldn't even care if we died because that would be emotion. It wouldn't bother us if we got hurt and we would value nothing. To a being with no emotions everything would be the same. To even have goals to carry out requires one to value something, which requires emotion.
It bothers me when people put logic and emotion in opposition. They can be, but often I would say they are not. Emotion informs what your goals are, logic is about facts that follow from premises. Emotion can cloud one's judgement and lead to a faulty conclusion, but if it merely informs you on what your premises are then there is no conflict with logic. For example if I wish to be happy, that's emotional. Then I can use logic to help me figure out how to achieve that state.