Cancer Research UK explains that a person usually feels cold and starts to shiver during the first phase of a fever as it's the body’s response to an increasing temperature. There are three phases of fever: the body's reaction to fever that results in heating, leveling off of the fever, and the cooling of the body.
Having a fever means that a person’s body temperature is higher than normal due to an infection or other causes, says Cancer Research UK. In the early stages of a fever, people typically feel cold as a response to the high temperature. The skin’s blood vessels tighten and force blood from the skin’s outer layer to flow inside the body where it is easier to retain heat. The outer skin layer then turns cool, and muscles begin to contract. This causes shivering, which creates more heat and raises the body’s temperature even more.
During the second phase of a fever, the body creates and loses the same amount of heat, states Cancer Research UK. This stops shivering and allows the body to retain its new high temperature. In the last phase, the body tries to return to a normal temperature by cooling itself. The skin’s blood vessels open again, and blood flows back to these areas. Sweating occurs to help the body cool.