That's actually not a bad idea. Another option is something like this:

http://www.amazon.co.uk/Prince-Lionh...cm_cr-mr-title

It is designed as a sunscreen for car windows. A plastic foil that sticks to the window by pure static force and holds tight as a tick (i.e. does not let go, can withstand opening and closing the window etc). Feel free to read my review. I've used it for over three years without a glitch.

It is a bit large but can be cut to size to fit a phone screen. The tint is light brown, not blue as in the Amazon picture. And it can double as a scratch protector too!

Of course, they may be similar products already tailored for mobile phone screens. Just have a look around.