During fever, why does only the tip of our fingers become cold? While the whole body remains warm

Mainly because the loss of heat is greater due to the fact that our body is hotter. Human beings have an average temperature of 98.6 degrees Fahrenheit. The brain (centre of brain called hypothalamus) monitors body temperature and controls our bodies to keep our temperature within the normal range. If you get a fever when you’re sick, it’s because your brain has told your body to get hotter. If the brain senses a rise in temperature, the opposite changes occur. This is accomplished by increasing blood flow to the skin, breathing faster and by sweating. (When your sweat evaporates, it cools the body.) If the brain detects a drop in temperature, it directs the body to make a number of changes to correct the imbalance. Those changes include increasing heat production within the body (by shivering, for example) and reducing heat loss to the environment. Heat loss is reduced by decreasing blood flow to the skin. So you actually feel coldest when the temperature is starting to rise and hottest when it's starting to fall.