It should be just fine to take them out. If the front window opens on the trailer, put a fly mask on him and leave it open (you can bungee it open if you need to, so long as its not big enough for him to get his head all the way out. Just enough to put his nose if he wants, but no more)
I normally wait as long as possible to boot and wrap my horse. Immediately take all wraps off after the ride, hose his legs down, and if you have time unsaddle and do about five minutes cool hose on the legs and then hose off his body nice and good. Also the sponge is a must.
Always have water available, and put some gatorade/powerade in it so he can have some electrolytes.
You can also hose him before he goes in the trailer.
Also, if you feel him shutting down on you, let him. If he is in shae he should be just fine with it, but I see a lot of people push their heat exhausted horses and cause problems. I just got back from running barrels at the biggest, longest barrel course in the world (Pendleton, it's a 30-40 second course) in the high heat. I saw horses come out of it with nose bleeds, frothing sweat, etc but none of the ones in our trailer did because of all the precautions we took.
Don't be afraid to warm him up in this heat! It's all the more important now, so he can be loosened up for it. Right before you go stop and walk circles, get his breath back but keep his feet moving. It will make all the difference to his lungs in the heat and humidity.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.