I observed this as when I want to cool my soup I blow like a whistle and when I want to warm my hands I open my mouth more as my breath is warmer now.
Your breath is the same temperature either way. The difference is how much ambient air is brought along with the breath by the time it reaches the object.
Emitting a thin and fast stream of air will cause a lot of other air to follow along with it. When you are blowing on the soup to cool it, what you're really doing is using your breath to move a lot of ambient air, which is what cools the soup.
When you breath on your hands to warm them, you are emitting a wide and slow stream and hold your hands close to it. The result is that your hands get mostly that original wide and slow stream without a lot of ambient air mixed in yet.