At night, the earth's surface cools by radiating heat off to space. The strongest cooling takes place right near the surface while temperatures at roughly 3000 feet are actually warmer than those at the surface. On a windy night, some of the warmer air aloft is mixed down towards the surface. This occurs because the winds are faster aloft than at the surface.
To visualize this, place one hand over the other about six inches apart. The bottom hand represents the air near the surface and the top hand represents the warmer wind higher up. Move the bottom hand slowly and the upper hand faster (to indicate the faster winds aloft). The faster air above and slower air below causes the air to overturn or spin (as in the picture below). This overturning motion is how warmer air from above is transported downward on windy nights.