temps shouldn't go over 75%, and humidity also has a play in that, personally i don't like to go over around 72.
when you get him in the travel cage, pls keep him out of direct view of sun, air conditioning that may be on, or an open window.
give him some stuff to chew on, eat, water if you can in the cage, and if you also can, cover the cage abit with something, something that isn't heavy so it will overheat him, but something light that will make him feel safe since they like to hide, .. or even if you just cover part of it.. i do that sometimes when we travel to the vet.
j