Hmm. It depends a lot on the variety. There are some that aren't very sensitive to how much sunlight they will get, some that like lots of sun and can't do without, some that actually prefer partial shade. If you get the regular sort of strawberries (either seasonal or day-neutral commercial types), shouldn't be a problem. Alpine strawberries won't usually put up with hot, bright sunlight though, they prefer a little light shade and slightly cooler temps.
Seeing as how most strawberries are indeed grown in 90+F weather (California, Florida, etc.) I don't think you should worry overly about them getting cooked. Watering is more of a concern, hot soil doesn't hold water so great. Mulch well with straw.
You know what the screening is usually for? Birds. Think Alfred Hitchcock-like plagues of birds, chasing you out of your own garden. And raccoons. And possums. And deer, whole herds of them. All in your garden at once, like Noah just opened the ark door for snacky-poos. Birds so bold that they don't mind a screaming hairless monkey waving a stick at them one bit. Birds that scare the neighborhood feral cat colonies into submission. Birds that could make a Rottweiler run yelping under the porch in submission. That's what un-screened strawberries will get you.
