There are several brands of storm doors with interchangeable glass/screens. I had two different types/brands and will never have another. Too much trouble changing and storing the glass/screen.

The advise about no storm over fiberglas is true---in some cases. If the door in question is facing north or east, there is not much worry. If the door is facing west and is partially shaded, the heat factor is lessened.

If the storm door is vented, the heat build up is minimized.

So, the answer pretty much depends on your door and the situation.

Here is a link that might be useful: Just one example

Thanks for responding, Handymac! Just found out from hubby that our full-view storm door has a full screen stashed in our shed from years ago. I guess since our house's door is at a west-facing, non-shaded site we'll be forced to use the screen exclusively. It's funny, I was thinking - before I read differently - that a storm door would protect the new door, glad I found out before I ruined the new door!! In fact, I'm now surprised the guy Home Depot sent out to measure for the new door & do installation didn't mention a storm door could be a problem.