How can I keep my MacBook Air's battery cool?

Apple only provides a few recommendations.

Use the computer on a hard surface:

Using the computer on a soft surface like a couch, pillow, bed, or your lap can trap heat requiring higher fan activity. Using the computer on a hard flat surface like a table or desk allows for optimal radiation of heat.

Don't block the fans:

Make sure the vents remain unblocked to allow your computer to perform at its best.

On the MacBook Air, the fans are located in back.

Speaking from experience, I would say that you should be cautious of running Anti-Virus apps which actively scan your computer. They are often resource intensive, and I've noticed that these apps can conflict with Spotlight and cause the CPU usage to skyrocket for a long period of time, which heats up the battery.