The heart and the mind essentially are two different things figuratively. We name them as heart and mind since it would be too complicated to define each of these each time a confusion arises.
The mind is the conscious and subconscious set of thoughts which are dependent and function on various parameters such as past experiences, society, upbringing, value system, etc. Whenever an action or a thought counters the mind, there is a processing based on the parameters and then the decision about right or wrong, bad or good, happiness, etc.
The heart is that part of our thought which is based on something which is termed as a "gut-feeling" or "hunch". Though a thought may seem ludicruous or wrong to the mind, it may seem as 'just right' to the heart. Usually, results of thoughts based on the heart may seem 'impractical' to humans, who are following many worldly based goals.
The main challenge is to recognise this concern, and resolve the confusion between listening to the heart and mind. Though the mind is one of the most important to listen to, I feel we must try and base the thoughts of the mind and the heart in conjunction with each other to get the best decision.
Many a times, we may struggle between the two, but I believe listening to the mind will give you all the material happiness and listening to the heart will give us the much required and essential spiritual happiness... because in the end, the body is transitory and its the soul that is forever...