The MacBook Air normally comes with a 45W adapter.
Apple makes two more capacities, the first one at 60W used on the 13" MacBook and MacBook Pro; the second charger is at 85W and is used on the 15" and 17" MacBook Pro.
You can certainly use the 60W and 85W adapters on your MacBook Air; it will not charge the computer any faster; it auto senses the computer that it's connected to and will adjust the output current automatically. The drawback to using the other two adapters are noticeably larger [and heavier] than the 45W adapter if you do travel.
If you're looking for another adapter, I would consider buying the 85W to keep at home. It is larger and heavier, but will charge any MacBook, MacBook Pro, or MacBook Air as needed. When charging the MacBook Air, the 85W will run cooler.
When you say cooler do you mean the brick doesn't get as hot?