There’s a degree of truth to this. Provided you aren’t ill, your body regulates your core temperature to between 36.5°C and 37.5°C. But your skin temperature is more variable, and results from a balance between how fast you generate heat from your core, and how quickly you lose heat to your surroundings.
If you keep your coat on indoors, it makes it harder for your body to shed heat from your core, so warm blood is pumped from your core to your skin to compensate, and your skin temperature rises.
The temperature that you perceive when you step outside depends on the difference between the temperature of your surroundings, and the temperature of the exposed skin on your hands and face. So since your skin is already toasty from wearing your coat indoors, it’ll feel colder against the cold air, you’ll lose heat faster, and it’ll take a minute or two before your body reacts and diverts the blood back to your core.
The benefit of taking your coat off indoors, then, is that you step outside with a lower initial skin temperature, and it doesn’t take as long for your body to acclimatise to the temperature difference. Plus, you can put your coat on to reduce any additional heat loss.
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