I think that 'fashion' or 'to old/to young' is out of the window when it comes to protecting yourself against the sun - especially in a hot climate. Dehydration and sunstroke are just around the corner when you're relatively comfortable in your car (it's not as physical as cycling, so you don't get warned by the fact that you're getting hotter and tired). Try to find something with a sunblock characteristic and perhaps a light colour as well.
I know that sailors wear caps made by Zhik, an Australian brand. Musto has a few lightweight, sunblock'ed and fast dry caps as well. When I'm on a 120 hp RIB and at full speed, I prefer a Musto cap. Last year, when I was really hot I changed to a Tilly hat, but that's not suited for an open top sports car, I think.
M