I think it's a good idea. No use making it any tougher on them then necessary. Before our club got a trailer most of us that hauled the races had toppers on our pickups. When they're in the crates in the trailer they're pretty well blocked from the wind but they still get a fair amount.
As humans, when we are outside in windy areas, we actually lose more hydration than most realize. Cold or hot..
When you take a new tree for planting even on a nice day, they tell you to wrap it. If a nursery is delivering trees, they are wrapped. It's not sun, or heat. It's because wind dehydrates.
I'm not saying put them in air tight, but for birds to give their best, you got to give them the best you can. I'm not saying buy a topper, but even a small wood cover for their boxes to sit in will do wonders. Have a large dog crate? (Plastic not wire). Set the bird basket inside the dog crate. Secure both.
I cut out a piece of tight woven carpet to fit the top of my cages with a slot for the handle, with a bungee cord. Works good, and it doesn't hurt to give them a drink of water while settling them b4 the release!!
Been hauling/training pigeons with car since 1984...Never had any birds die,or get sick from being in a trunk of my car...It`s dark,and they stay quiet,and don`t fight....I used to put them in the back seat....All they did was fight and carry on....That`s how you get birds pecked in the eyes....In the trunk,it`s quiet time and rest...No air problems....Now,I always train in the mornings,so it`s not that hot....If you train in the heat of the day,you might want the trunk lid open a couple of inches....Alamo