There is no difference between these two constitutions. Heat represents yang, and cold represents yin. Whether people with hot constitution like cold or people with cold constitution like heat, they all spontaneously reach a state of cold-heat balance and yin-yang balance. I know this just to know myself better. You should choose your lifestyle according to your own physiological laws, and don't try to be brave.
Pay special attention to physical factors when you need to take care of yourself when you are sick. Our Chinese medicine is in place in this respect. For example, people with cold constitution should not use laxatives too much after getting angry.