In order to initiate a fever, your brain actually turns up your body’s thermostat- setting the target body temperature higher than normal.
This is interpreted by your body as hypothermia- after all, your normal temperature of ~98F is now a couple degrees colder than the new target of, say, 101F.
As a normal response, you feel cold and your body responds accordingly by constricting blood vessels and initiating shivering to generate body heat and reach the new setpoint temperature.
Latest Answers