The thermal receptors in your fingers measure their own temperature, just like a thermometer. When you’re touching an object like a mug, which conducts heat poorly, it takes time for the heat to make its way out of the mug and to the receptors in your fingers, meaning you sense it rising slowly because it *is* rising slowly. If you touch a piece of aluminium at the same temperature you’ll get burned instantly because the heat transfer happens much faster.
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