If you want to reduce the flapping and don't need to fold up the top when removed, here is what I did with my top.
You will need the following:
Insul-Bright insulating cloth at Joann.com
Black vinyl or any color that you can find on clearance
Contact cement (Weldwood original)
On a warm day in the shade, remove the top and stretch it out as smooth as possible. Might want to make a rig and used bungee cords to keep it taut. Cut the insul-bright and vinyl to cover the flat part of the roof area. I did this in sections so that if I did screw up applying the insul-bright, it would be in a smaller area.
Then brush on 2 coats of the contact cement on the top and the insul-bright following the directions. Then place the insul-bright on the top. Be very careful here to make sure that you get it lined up correctly the first time as the contact cement is called this for a reason.
Then do the 2 coats on the insul-bright that you just attached to the top and to the vinyl, and mate them together. Now let it cure overnight and you will have an insulated top that will not flap.
Did this on my half-top and another bikini top and it worked great. The insul-bright has a foil center and the shiny side needs to face the direction you want to reflect the heat. The caveat on this is that the top will no longer fold up into a nice package any more.