Actually - a hot shower works much better to cool you down...learned this a few decades back and it always works. The reason? Your body's default setting is homeostasis - a point of balance, whatever it's 'normally' supposed to be doing. Like maintaining a constant temperature. Although you FEEL hot, your internal temperature is the same as ever. But when you have a cold shower, your body perceives this as "uh-oh!! I'm cold! Gotta warm up!" and it will make you feel hot once you turn off the cold water.

You know how when you burn your finger, you stick it under cold water for a couple of minutes and it stings like hell when you take it out? That's why. Your body recognizes all that cold water and sends heat to that area. Instead, run it under water that's as hot as you can stand for a few minutes. It'll sting a lot less when you turn off the tap.