You don’t actually feel temperature, what you feel is the heat transfer to or from your body and your surroundings.
That’s why putting on a jacket makes you feel warmer. It’s not warmer than the surrounding environment, but you’re no longer having heat flow from your body because the insulation lets you retain more of your body heat.
The greater the temperature difference between you and your surroundings, the faster the heat loss will occur. So if you have an elevated body temperature, you feel more heat loss in a room than you usually would simply because heat leaves your body faster.
This is also why women feel the cold more. They have a higher basal body temperature, so they are bleeding more heat into the surrounding air than the more cold blooded men around them.
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