There are solar control films that might help with the radiant heat.

Stay with the big companies like 3M and similar.

You could look into getting an Aerolenz Skylight Insulation System. We were going to get them for my parent's skylights, but they ended up replacing their skylights.

Here is a link that might be useful: Aerolenz

@Windowsionwashington: I thought about the film, but since it's not a flat surface, it didn't seem like a viable option. Can that work?

I don't think Aerolenz is an option since I live in a condo, but thanks for the suggestion.

If a professional installs it, I am sure they can wrap it on a curved surface. Most cars are curved windows and they get that stuff to lay down just fine.

What about putting the film on the flat interior?

I put a pleated shade on my skylights that pulled open and closed with a long hook. The have a track on both sides. They were relatively cheap and are great for keeping out heat. My sister-in-law did the same on hers.