When you are overheated, it causes your blood pressure to rise a little. If your nasal mucosa has more vasculature than the average person, then the vessels leak out blood, hence a nose bleed. The way we coll off is to dilate our superficial blood vessels in the skin. That is why we sweet. It is a way of cooling the blood inside your body. Unfortunately, when vessels dilate to cool you, the vessels in the nose also dilate. A dilate vessel has more blood flow and sometimes the small capillaries break and bleed. It is usually hereditary (the nosebleeds) because of the extra capillaries in the nose. Pinch for 2 to 3 minutes and keep the nasal mucosa well hydrated by using petroleum (like Vaseline) at night to keep the blood vessels from being brittle.