Quakers ar3e pretty good at dealing with heat. They are tropical birds to begin with, so they are inda programed to deal with warm temperatures.
Here in Kelowna, in the summer, teperatures regularly get into the 90's, and with no A/C, ours do fine.
The trick is to keep them out of direct sunlight, give them access to water, and watch for signs of overheating. Those signs include panting and holding their wings away from their bodies.
I'd be more concerned about insect bites, particularly mosquitoes. If you are travelling to an area where there have been cases of west nile, bring mosquito netting.