You don’t feel temperature itself so much as you feel change in temperature.
You feel cold in cold weather because the air is constantly sucking your body heat out of your relatively hot body. In weather around 75 F° or so (I don’t remember the actual temperature), the heat you’re losing is the same as the heat you’re generating, so you barely feel temperature at all.
When you have a fever, however, your body is much hotter. This means you have more heat to dump into the surrounding air, so you’ll feel colder than you normally would in the same air.
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