What you Need
What to do
Hold your hand about 15cm from your mouth
Purse your lips and blow at your hand
open your mouth and blow on your hand.
Do you notice a difference in temperature?
Now try holding your hand very close to your mouth when blowing with pursed lips or a long way away with an open mouth.
What may happen
You should find that at 15cm your breath feels cold with pursed lips, but warm with an open mouth.
But if you feel very close with pursed lips it feels warm and cold when you feel a long way away, even with an open mouth.
Why does it happen?
If you create a jet of fast moving air through stationary air it tends to drag the stationary air along with it, essentially due to friction. This is called entrainment, and the effect is stronger the faster the air jet is moving.
When your mouth is open the air coming out will entrain some cold air, but the air which reaches your hand will still be dominated by the warm air from your mouth.
But when your blow hard through pursed lips the jet is moving a lot faster so it entrains more air, and there is less warm air there to start with, so most of what reaches your hand is colder room air. Although this air is slightly warmer than the air in the room it moving so it is much better at removing heat from your hand both by conduction and evaporation so it feels cold.
If you feel the air coming out of your pursed lips very close to your mouth it hasn't had time to entrain cold air, so it still feels warm
And if you feel the air from an open mouth a long way away it will have entrained enough air to feel cold.