The human body becomes hot during and after exercise due to a chemical reaction caused by the muscles burning fats and carbohydrates. Muscles produce an energy, and some of it is not efficiently turned into mechanical energy. According to HowStuffWorks, this leads to excess heat within the body.
HowStuffWorks explains that blood vessels then dilate because of this excess heat, causing an increase in blood flow under the skin. This heat then evaporates from the skin into the air. This is why skin feels hot during or after a workout. This heat also causes the pores to sweat in an attempt to lower the body's core temperature.