Is that a Glass one?
Mine, the roof is opaque white plastic, triple layer stuff. 1.5″ thick. My South facing wall is solid Brick (It’s a boundary and I can’t put a window in it). It’s supposed to keep that sort of heat out.

We’ve gone over the top with the building regs, I’ve got 3 inches of foam in the South Wall, the stub walls that are under the windows and within the concrete floor. Interor walls are all Thermolites. This lot should also aid temp. regulation.
It’s a single pitch roof up against the house, the highest point (House) is about 9 foot, so it’s airy as well. I will put a thermostat in there and keep a watching brief, especially as we are expecting a scorcher of a summer. (The Frogspawn is in the middle (Over the deeper water hence last longer in a drought), the Frogs long term forecasting is better than the Met office). And I know the Spawn will be gone by Summer.

Come September, the Bold words will be used against me!

We have a glass roof and it is east facing so it gets the sun from morning until about 3pm. You might be OK with your arrangement. As long as it doesn’t get too bright to see the screen!