Thou the wind is moving faster, and feels cooler to the touch, it’s not a different temperature.
The cooler/warmer feeling from touching things like metals or moving air at ambient temperature is due to the faster transfer of heat.
The thermometer will still be able to accurately measure the temperature of the air, even more quickly, while the air is moving.
Actually, having the car not moving is more likely to provide a less accurate temperature reading. The air staying stagnant in the area of the thermometer could be heated by the pavement or engine. If the air isn’t moving, that warmer air is sticking around a while.
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