I am generally against any insulation in a coop. When I started out I was determined to insulate that puppy within an inch of it's life - being in Northern Wyoming near Yellowstone Park our winters can get pretty brutal. But calmer heads prevailed, and we ended up with a coop that has tons of good passive ventilation in winter and passive and active ventilation in summer, and my birds did extremely well in their non-insulated, non- heated coop. Not even a case of frostbite. (Well, except for one little chick named Scout, but that's a whole 'nuther story!) My coop is a wooden one we built ourselves.
However - you are planning to use a metal shed, which presents an entire new set of logistics to consider. It will get hot, hot, hot! So what the other posters have said cannot be overstressed - ventilate and ventilate well! And using a metal shed is one place where I would use insulation, just as Klopklop and Bryant Redhawk said. Don't forget shade. If at all possible, locate your coop where there is some shade...invent it if you have to. Maybe draping some kind of fabric over the entire setup. Landscape fabric works very well to provide shade because air flows through it and every cooling breeze is a help. It's cheap and if it rips, it's easy to replace. You could put a few posts in the ground, attach the landscape fabric, and drape it just along one side, or maybe even tent the setup with it. Of course, natural shade is best, but any port in a storm, right? Without seeing the area you intend to use, it's kinda hard to advise on shade, though. I use landscape fabric and am a strong proponent of it. I have it attached directly to my run, but don't have to shade my actual coop so I'm not sure how that could be done, but I'd sure look into something for shade. A metal shed in the hot sun isn't much different than an empty soda can in a parking lot in the sun! Truth be told, chickens suffer much more from heat than they do cold, as long as they have a draft free but ventilated coop.
Another thing you might look into is an exhaust fan located up high on the walls. If you go to a site that carries parts for older mobile homes, (and they exist, believe me - it's all that keeps this old trailer we live in habitable and still looking good!) they have them. The reason they are ideal is because they have a chain and a motor. They are also designed for the thinner walls that old mobile homes were constructed with rather than being based on 2x4 or 2x6 construction, which means they fit well into the kind of walls we have in our coops. Ours was rigged so that we can either use the chain to keep it open without the motor running, which we do all winter, or have it open and running in the summer. A couple of low vents in the coop and that exhaust fan pulls stale, moist air right up and out, replacing it with cooler, fresh air right at chicken level. Love it!