United doesn't allow pets as baggage anymore, but they do ship them as cargo. More expensive, but better tracking and handling, and there doesn't appear to be any temperature embargo except for out of Dubai in the summer.
http://www.united.com/web/en-US/cont...s/default.aspx
Obviously, nonstop travel is best when possible.
If your friends can travel separately, having one go ahead so that they can be there when Fido's plane lands is ideal. Or leaving Fido with a friend and asking that he be shipped a few days after they've arrived would be another option.