Answer
When you breathe on your hand, the temperature of the exhaled air reaching your hand decreases.
Work Step by Step
Note: the book's answers on page S-1 say that whether the temperature goes, down, up, or stays the same depends on how you blow.
However, we disagree. The air you exhale expands, so the temperature goes down as the air does work on its surroundings. If you breathe out with your mouth open, the air expands less and will feel warmer than if you blow out with lips pursed.
Nonetheless, in both cases, the air is still cooler than when it was in your mouth; there is no physical mechanism for the temperature of the exhaled air to rise.
This is discussed on page 305.