American Airlines doesn't allow pets to be travel by plane when temperatures are too high.
Other airlines may have similar concerns. I've read where smaller pets can sometimes go under a seat. Even when checking is permitted, I am not very happy with checking a dog into the cargo bin.
Did you know you can go to a self-service pet wash? Dippity Dog offers this service. It's in Oceanside but just north of the Carlsbad border on the east side of El Camino.