The short answer is these heat shields probably make the air entering the engine hotter. They make an engine lose power.
Testing Cold Air Intake Heat Shields
I have done testing of different layouts of heat shields for a performance cone filter. The conclusion was for the cold air intake heat shield to be effective, it needs to completely seal the air filter from the engine and exhaust heat, no gaps.
I found when using a heat shield similar to the photo above, the intake temps were generally higher than with the standard air box. And when the car was moving the intake temps dropped more slowly than with the standard air box. I presume because air was being pulled from the engine and exhaust and because the cold air from the front of the car was being blocked by the heat shield.
Shields like the one above, are in my opinion, the worst of all worlds. They allow hot air to be sucked into the intake and they block cool air from getting to the filter.
Worst Case Usage
Perhaps if the filter of the cold air intake was mounted right next to the exhaust or turbo, putting something in between would help, especially if the area didn’t get a supply of cool air but in situations like this, the answer has got to be to move the air filter.
If you are buying a heat shield like this for looks, which material is best?
Definitely the material that conducts heat the least. Worst material would be metal, the best material would be carbon fibre. In between would be a plastic that can withstand the heat without melting.