Can't say I believe fitting the film externally would make much difference as far as heat rejection goes but I did do it on one of my vehicles many years ago. Here's why:
I had a '94 Toyota HiLux Surf/4Runner that I had tinted with a 20% film.
Back then Toyota installed light bronze glass in a lot of their vehicles instead of green, so a 20% grey film looked quite nice on most of the windows........ except, the cargo windows, which have a reflective coating from factory on the inside.
Now no film, no matter how black it is would make those windows look particularly dark, so I tinted them on the outside instead.
This had a much better appearance and blended with the rest of the car.
I had it on there for months without it ever peeling off.
I even drove across Australia, from Perth to Brisbane and down the east coast through heat and snow at times and it held up well, until..... after a month on the road the vehicle was looking a bit crusty, so I gave it a good going over with my pressure cleaner. The scratch resistant coating started to come off and looked like crap so I peeled it off and never bothered replacing it again.
So whilst this has not helped the discussion about heat rejection, it shows that it can be done.
And by the way, I spent some time in Dubai a few years ago and noticed that many cars had their back window film installed on the outside.