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It will help a bit but sounds like you have the same problem as me where the plastic touches the SS supports. I put some 15mm pipe tube insulation around mine (when I got a new screen) and it looks ok and after two years no sign of burning.
Or, instead of pipe insulation, a strip of the cover material, or canvas of same colour, velcroed down the long edge and wrapped around the SS length which touches the plastic. Found 4 of these buried in a locker after buying the boat - previous owner didn't know what they were for. They work a treat and look pretty good.