We don’t detect temperatures like a thermometer based on how hot or cold it actually is, we do it based on how slowly or quickly heat enters/leaves the skin.
This means if something pulls the heat out of us faster, it will feel colder. And if something pushes heat into us faster, it will feel hotter.
Carpet insulates very well, so heat transfer will be much slower compared to a wooden floor, which will be slower than a tile floor. So a carpet will feel warmer than wood, because it pulls the heat out slower.
On the flip side, if the floor was heated up to like 50C, much hotter than your feet, the carpet would feel the coolest, because it would push the heat into your feet the slowest.
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