There are two competing effects when a human stands in the wind.
One is that the air flow does indeed make the air hotter, and the total air temperature (TAT), which includes both the "static" air temperature (SAT) and the kinetic heating (or ram) effect, will be therefore slightly higher than the static temperature. However, it's a tiny effect at typical wind speeds:
A 66 knot wind at sea level (which is a LOT of wind!) would create a temperature rise of about 0.2%, or about half a degree Celsius.
The more important effect for a human sensing temperature in the presence of wind is the effect that the wind has on the effectiveness the air has in heating up or cooling down the skin - the effect normally called windchill.
Higher wind speeds make the air more effective at cooling - or heating - the body. Because your body is typically at close to 40 deg C, whenever the air is cooler than this it is, in fact, cooling you down. So the harder it blows the more it cools you. This effect is more powerful than the kinetic temperatuire rise due to the wind speed, so overall, a wind chills, or cools, the body.
Note that for an object which is not heated, or temperature regulated (which is more or less what the human body does) the windchill effect will bring the object to the stable temperature faster - but that temperature will be the TAT, not the SAT. (And definitely not the "windchill" temperature, which is a fictional "feels like" temperature)