Answer:
Sweating secretes fluid onto your skin. As the heat in your body excites this fluid (heats it), it draws energy out of your skin and causes the fluid to evaporate. Since it is drawing thermal energy out of your skin, it cools, thus cooling the blood vessels in your skin (which are dilated due to your increased temperature). The effect is your skin cools and so does your blood. As the blood is pumped back towards your core, your core temperature drops.