This occurs not only when we exercise but many times when we have a fever or basically recovering from one. Our blood like many other fluids has an optimum temperature and pH value to make all those reactions occur in the body. When the body is subjected to stress as in this case; exercising, the blood pumps rapidly in our veins making the veins dilated or bigger. This is because more oxygen is required for respiration as rate of activity increases, thus more blood is required. The body temperature rises due to more energy which is made while breaking glucose (respiration) thus the temperature of the body rises. Now the Almighty has created everything systematically with no mistake; the veins come closer to the skin (as you may have noticed while exercising or on a very sunny day) and sweating occurs to cool down and lose all that extra heat energy to the surrounding which otherwise could be dangerous for our bodily functions. How it may be dangerous is because if the temperature would have remained higher it would have broken down the enzymes in our body that are essential for all reactions in our body. That is why we human beings (Thank God) are warm-blooded (have a constant body temperature)
When we do exercise then blood circulation speeds up and make our body hot. Blood is like a petrol for our body which makes us alive. Like a car when it runs fast, it becomes hot. Similarly our body becomes hot when blood circulation speeds up. The normal temperature of human body is 37 Centigrade which is because of our blood circulation.