Blood flowing through the circulatory system heats and cools the body. Wben your temperature rises blood vessels expand and are close to your skin, and sweat is made. This is heat escaping the body. When your body is cold, blood vessels get smaller and help you retain heat.
You are exactly right! When we get red-faced after exercising, it's those dilated blood vessels in our skin trying to cool us.
I agree with Shane, and to add on to that I think that your heart pumps blood that helps bring oxygen to your muscles to help them to not get so worked up, and thus you don't get tired as quickly. Also, if you are cold, the blood rushing through your veins can warm you up.
And if your muscles are overly cold, or if your body is overly cold, your circulations slows (to keep enough blood near your heart), and your muscles can cramp or you can develop hypothermia as a result. Our systems don't work well when we are not at homeostasis.