Apollo
It's not like the god was emotionless... just look at his long line of male and female lovers.
To be without emotion is beyond human beings, more than likely.
I could also say that to be without reason is also beyond humans, at least a sober human being.
Perhaps we could say that someone who has gone completely psychotic is without reason (or at least appears so).
I could argue that there is a difference between totally objective (and thereby having difficulty making decisions where intuition, common sense, or human values come into play) and being logical.
Being logical involves objective thinking but a well balanced person, I would think, factors in human values, as well, (compassion? mercy? etc.?). A well balanced person sees logic as only a tool to becoming a better person and a tool in making good decisions. Certainly to disregard either logic or emotion entirely as good means to a good end would not be prudent.