I fly blanket my girl in the spring/summer. It saves me on flyspray!!
I've tried the weatherbeeta airflow mesh...it was nice but it didn't stay on well, she ended up ripping it...long story...but it was a NICE blanket....
I currently have the Amigo Bugbuster. It's a VERY NICE sheet. It's very soft but strong. Stays in place and keeps the bugs off. Nice sheet overall. Looks funny, but serves it purpose very well!!
My girl would roll around many times a day in this sheet and it always stayed on well. Keep in mind, she's a draft horse, so she really put the stress test to it! I love this sheet!! I've got pictures...she looks soo funny!!
As for getting hot, the sheet ( a good sheet ) actually is supposed to help the horse stay cooler. It reflects the sun off the horse. My girl wore her Amigo sheet in high 90 degree/100 degree weather. She seemed content and I don't remember any sweating.
I've seen the cheaper mesh sheets though, and unless your horse is gentle on blankets, I wouldn't recommend them .