Do I need to protect my leather saddle from the sun?
I'd think a white opaque plastic bag over saddle would do fine.  The leather has to breathe - if you wrap it tightly then it might grow mould.
You might have to treat your saddle leather a little more frequently if it lives in the sun/heat a lot.
Ideally, store your bike inside, a garage, or at least under some rain protection.  A balcony/porch/etc is better than out in the weather.   A wall-hook or lift might let you utilise unusable space.