I'd have to say heart and intellect play a lesser role in dancing well. Determination and natural ability are the most important. Although, I'm not sure what you mean by "heart and intellect". If you mean by 'heart' a desire to do well and the courage to keep trying, then yes, heart is important. Intellect? Do you mean an ability to learn? Then again, yes it's important. That being said, I know some very good dancers for whom dancing comes as naturally as breathing. One is as dumb as a post. Intellect does not come into play. I suppose I could be described as having heart but it doesn't help my dancing much. I am not athletic and will never be a great dancer. I am well aware of my limitations. As a fellow student said to me, "I dance much better in my head." In our cases, heart and intellect does not produce the desired results.