During a fever your body’s core temperature rises to a degree that can harm all the organs. To prevent this your blood vessels restrict so that less blood can flow through at once. This is to help your body cool down. Therefore even though your core temp is higher, what you feel is the warmth of the blood flowing through your veins and vessels since it’s closer to your nerves and skin. It’s the same concept as feeling cold even though your body temp is normal!
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