Hey! As a seventeen-year veteran of a summer Renaissance Faire, and a fellow Hetalia cosplayer, I think I may be able to help. When we cosplayed Hetalia for the first time, it was July. We hadn't forseen the weather like you are, so we were stuck with our hot costumes (mine - I'm France - and my Russia's is lined with satin, even.) To begin with, I tried not to wear my gloves unless I absolutely had to. My Russia kept her scarf on the whole time, but the huge thing is great for hiding ice packs. If you want, you could press an ice pack to the back of your Russia's neck (make sure it's mostly just cold, rather than frozen, or that it's wrapped in a towel to avoid frost bite of any sort) and hide it with their scarf. Manada and England might be harder. Try to avoid wearing anything unnecessary under your outfit. If you're binding, especially, make sure you take time to unbind and cool down. In July, the whole group of Hetalia cosplayers took off a few layers after the shoot and sat inside to cool down.
I really can't suggest many ways to avoid the heat other than taking breaks, remaining hydrated, and keeping an eye on each other. Carrying an ice pack with you might be a good idea. If not, you can try a wet towel. Those work until they warm to match your body temperature.
...That wasn't as useful as I had hoped, but I hope you got something from that! Best of luck!