There are many ways by which a healthy human body deliberately dissipates heat. First, it is important to note bodily temperature is not uniform. Our skin is generally colder or warmer than the rest of the body, which is the reason why we place the thermometer between our armpit or inside our mouth, instead of just placing it in our say, fingernails.
Arterioles can tighten or relax, increasing or reducing blood flow. High CO2 concentrations and heat cause the arteriolar diameter to increase, allowing larger blood flow. High oxygen concentration and cold cause the opposite effect. At normal conditions, about 0.2 to 0.5 liters of blood pass through the skin. But under stress, this can rise up to 8 liters per minute. What this response entails is an increase in cardiac load.
We have up to 4 million eccrine sweat glands. Normally, they secrete an extremely filtered version of blood plasma, which is odorless. Exercising or heat changes this. As it is mostly water, which has a specific heat of 4.2 joule per gram, its evaporation releases quite a bit of heat. So what this mechanism requires is greater hydration, or else there is risk of hyperthermia (increase in core body temperature unrelated to fever).
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Physiological Responses to the Thermal Environment