I guess different geography requires different methods. I had to think back to my visits to AZ and Phoenix, you don't have much shade. When I am at home in CT, most of my favorite roads are tree lined and shady. On those really hot days at home, maybe if I had a half helmet that worked well, I might wear it.
My interest in a half helmet is for summer rides in Ontario, last year I was just dying in my full face helmet. Even a 5 min trip and my head was drenched at times. They've got a helmet law, so need something, plus their streets and highways aren't exactly tree lined either.
Cover is good, with a lighter color half helmet, the top provides shade, they usually even have a visor extending over the shield probably providing more shade than a full helmet. The added airflow has got to help the rest of the head. I haven't found a full face helmet yet, that those fancy vents actually do much.