While a coops primary duty is for night-time roosting, in almost all cases they are called on to be daytime shelter as well, if only because it's raining, too windy, you're out of town, someone forgot to let them out, whatever.
So the ability of the coop to provide the best possible conditions cannot be simply dismissed by saying, "oh they'll never be in there during the day".
To create the best possible conditions, regardless of the coop size, orientation of the coop is critical. Let's deal with both extremes (hot and cold) and see what we can come up with.
Heat first.
With few exceptions, chickens don't like direct sun and spend the vast majority of their time in the shade, especially in hot weather, so you're correct, a clear roof is a very bad idea.
In fact, the best possible roof in hot weather is a bright white roof, to reflect as much solar energy away as possible. I had a black PVC roof membrane I installed on my chicken tractor, and it got so hot, I could not touch it. I repainted it bright white, and the same membrane was cool to the touch, so in heat, use a light colored roof.
Next provide generous eaves, one foot to three feet, depending on whether you want to store things under them, and work beneath them, the benefits are many.
Eaves keep rain off the wood of your structure, preventing rot, they prevent blowing rain from entering windows, which allows you to leave windows open on hot humid days with storms, which is a huge help with ventilation and keeping litter dry.
As mentioned, they also give you space to store bins, and to work without getting wet, plus additional dry shelter for the chickens in the run, or keeping space under the coop dry in blowing rain.
Plus, for all these benefits, eaves are cheap. You've already built their support (the coop itself), all you have to do is simply extend the plywood, or whatever else you're using for the roof, beyond the walls of the coop as far as you feel you can, without the roof sagging.
If it's a large structure, pick up some covered storage space. I made the eaves at the back of my tractor 28 inches and now I wish they were 36 inches. My front eaves are 12 inches, and again, I wish they were 36 inches, especially when I'm working at the front of the tractor, with rain water flowing off the roof onto me.
28 inch, always north facing back eaves.
12 inch, always south facing front eaves.
I'm actually probably going to change out this roof membrane eventually, and carry the new membrane down 18 inches lower, along the sides of the tractor, then use angle iron to tilt the extra membrane up, creating a nice eave down each side of my tractor.
While your coop isn't on this scale, the benefits of eaves are just as true for a 4x4 coop. I'd guess good eaves could double the lifespan of a wood structure by keeping the wood dry.
You'll also notice I only allocated two feet of the 16 foot length of this tractor, to clear roofing, and it's only on the south end of the tractor, to capture as much low hanging winter sun as possible, to provide warmth to the tractor and the chickens in winter.
So that brings us to cold. In winter the sun is very, very low in the southern sky. In summer the sun rises almost due east, traveling directly overhead, then setting almost due west.
Most people aren't that aware of this fact because it has little bearing on our modern life of central heat and air.
But this natural fact is the greatest resource available to you, and your chickens, for a creating a comfortable coop.
Because all your heat load in winter is on your south wall, face one wall of your structure south to southeast, with as much glass or open wire as possible on this wall. This floods the coop with winter sun. However, in summer all the heat loads switch to your east and west walls.
Especially if you used eaves, no sun will enter the south wall of glass at all during summer because the sun is too high in the sky, unlike the winter sun, which is very low in the southern sky, and will flood the inside of your coop with sunlight.
So if you used eaves, in the summer, when all the sun is on the east and west walls, the eaves will keep the sun off your east and west coop walls, except early in the morning, and very late in the evening. This is a huge help with keeping the coop cool.
So ideally, your south side is open, and your east and west walls could have simple hinged wall sections that open, near the roof line, covered in half inch hardware cloth, under the eaves, which can be opened in the summer, even in rain.
As an aside, if you happen to live in a very temperate climate, like some parts of the southern US, and it seldom gets to freezing, you don't need walls at all. Ideally, you'd have half inch hardware cloth on all sides, with large eaves all around, keeping the coop dry and preventing rot.
To recap, use eaves, and provide as much open wire or glass facing south to southeast as possible.
