Final answer:
Sweating is the primary mechanism that prevents the body from overheating during strenuous exercise by increasing sweat gland output and utilizing the evaporation of sweat for cooling.
Step-by-step explanation:
When you exercise strenuously, the mechanism that keeps the body temperature from rising excessively is sweating. Sweating is a form of thermoregulation where the sweat glands increase their output in response to the increased exercise and body heat. As the sweat evaporates from the skin, it carries away heat, thereby cooling the body and preventing excessive increases in body temperature, a condition known as hyperthermia.
Other mechanisms such as dilated dermal blood vessels also contribute to heat loss by allowing more blood to flow near the surface of the skin, where the heat can be more easily released into the environment. Shivering and constricted blood vessels are responses to cold, not heat, and are not used to cool the body down during exercise. Rapid breathing can help regulate pH levels and remove increased carbon dioxide, but it is not the primary method for controlling body temperature.