Not sure why you don't want to make the opening bigger? There can be legitimate reasons, just don't know what yours are. I personally like openings that all can use, that allows me the flexibility if I need it for another purpose. I've had full-sized-fowl hens use a nest opening 6" high and 8" wide. Not sure a 5' x 7" will exclude much. That depends on what you want to exclude but. yes, chicks can certainly use it.
My electric netting has vertical strands every 3". The height of each level varies, starts out pretty close at the bottom and gets taller as you go up. I'm not sure what the height is where they go out, they can hop up some and it is flexible, not rigid. But my full-sized fowl chicks can go through this netting until they are around 7 weeks old. Broilers grow faster, bantams are going to be smaller. With the sides flexible I can't give you a specific size of opening and age but the openings probably don't need to be real big.
Have you checked the temperature on the floor where the chicks are? That's the critical temperature. Hot air rises so it might not be as hot as you think down there. Having high vents can help with that plus having an opening where cooler air can enter is a big benefit. I'd probably put an opening at ground level, covered with hardware cloth for predators, on the north side in the shade. That's probably the coolest air you have around.
This could be a good place for insulation, at least on the sunny sides, south and west in Knoxville. The sun heats up the metal and the heat can radiate out into the coop/brooder. They will eat many kinds of insulation so if you use a foam or fiber type, cover it. But just a piece of plywood either on the inside or outside could be a big help. Wood by itself is a good insulator. This could make a huge difference.
I regularly brood chicks in a brooder in my coop, often when the outside temperatures are below freezing and occasionally in the heat of summer when it is over 100 F. The +100 F is more of a challenge. In winter I try to keep one end warm enough in the coolest temperatures and another spot cool enough in the warmest temperatures. I find that chicks straight out of the incubator or from the post office are pretty good at self-regulating heat. They move to a comfortable spot. I don't know how many chicks or what breeds you plan to brood in that 8x8 building. I don't know what the outside looks like. All this might have an effect on how yours self-regulate. Also, sometimes when I open a door from a coop to the run, all the chicks might be in the run within 15 minutes. Sometimes it takes three days before they all are venturous enough to go outside. Each brood is different.
For what it is worth, this is my brooder in the coop. It's elevated and I have a wire bottom to it. In summer that wire bottom gives good ventilation. In winter I put pieces of plywood on that wire to help keep them warm. You may notice that the back wall of the brooder and the coop is metal. That's the western hot exposure. I do not put any insulation on it. It can get really hot on a summer afternoon but I haven't lost a chick because of that. This is a different situation than yours but it's part of why I'm questioning how hot it really is where your chicks are.
