Hi all,
I feel like I’ve read a lot and, like many things in life, I end up still being unsure what the right thing to do is.  I’ve got to reroof my bungalow, and that is going to happen soon but not immediately.  It’s a 1.5 story side gable home. I’ve attached a picture, I think, from the front. It has one dormer on the front, none on the back.
The upper rooms get very hot in the summer. There are effectively two rooms there, and one of them was remodeled before we bought the house and has cathedral ceilings.  There is no vent on either side, and the cathedral ceiling side cannot be vented even if I wanted to because of that.

I keep thinking that putting down two layers of rigid foam on the roof before whatever roofing material we use would be helpful for keeping the upper story cooler. But then I read, here I think and elsewhere, that if you’re not going to do a super sealed roof structure, don’t bother and just let it be open. Of course being open is not really a choice because of the way the gables and the Cathedral ceiling are conspiring!

Any clear advice on this? I’m sure that this has been answered 100s of times on this site, so please forgive and feel free to redirect me if this has been answered clearly in another Q&A.
Thanks!