Exterior Black Out, or Vinyl

I got a job lined up to do the dining area of a local pizza place, and the dining area is not the problem because I am using Johnson's Dn 20 and having Johnson's cut it to size for each window. The issue at hand is that they built a womens restroom on the west side of the building and in doing so they painted over the interior windows and then sheetrocked the inside. From the inside the bathroom is completely finished off and you would never know there was windows on the other side of the sheetrock. But in the late afternoon the customer said that the temperature in the restroom is like 90+ degrees.
I was wondering what kind of exterior film or vinyl would be the best to keep the heat out? I have black out left over from another job, but will it hold up outside? I do signs also and could use flat black vinyl, but would that keep the heat out of the restroom? Also I am trying to keep the cost of materials down also, I only charged him a little for the bathroom area because I figured I could use vinyl, but now I'm unsure what to use.

Black absorbs heat

Use white out or white vinyl

So if I installed a matte white vinyl do you think it would help block out some of the heat?

Matte White? No, it does not reject much energy. However, white as in Llumar NRMW-PS3 rejects about 72%.

I use mostly Suntek and Johnsons for my commercial jobs, I'll call them tomorrow and check if their whiteout is recommended for exterior use. If not I might have to try the LLumar, I checked out the specs online and it says the one you recommended is good for exterior use.

The Llumar NRMW is not exterior.

Well there is no way to access the windows from the inside unless we tear down a wall, so my only option is an exterior application. Any other recommendations?

I believe hanitatek and maddy have exterior films, tell em to send you a sample roll to try out