Most airlines that carry pets place temperatures restrictions (or embargoes) on pets going into and out of many airports during the summer. The best airline for summer pet travel is Continental, as they allow pets to travel year-round in climate-controlled comfort.
However, during the summer months, even Continental will embargo pets from traveling in and out of Phoenix due to the extreme temperatures Arizona faces in the summer. This embargo will begin June 15, 2010 and will last through the summer (likely until September). Pets will only be able to fly into and out of Phoenix before 9 AM or after 9 PM local time.