Why is breath sometimes cold and sometimes warm? (”hoo vs. haa”)

Hold your hand about a half foot (15 cm) from your mouth and open your mouth wide and blow air like you are fogging up a mirror. (”haa”) Your breath should feel warm. Now purse your lips and blow out. (”hoo”) Your breath should now feel cold. If you bring your hand closer to your mouth by about a centimeter away and blow out through pursed lips then your breath should feel warm again.
Why is this?

The air from your exhale is generally warmer than the ambient air outside your mouth. When your lips are pursed then the air is moving at higher speeds than with your mouth open. At these higher speeds the air from the exhale drags along the cooler still air due to friction. The breath air thus is doing work on this cooler so it also looses energy resulting in lower temperature. So overall the added cooler air and decreased temperature makes your breath feel cooler.

At distances closer to your mouth the warm breath air has yet to lose enough energy or drag along any cooler air so the breath still feels warm. With your mouth open the air is slower and takes up a larger volume so the majority of the air that reaches your hand is warm.