I like to find the simple solutions first; Is there not a spot that is mostly shaded that you could park your bike? Perhaps, move to another spot during lunch to "chase" the shade.
As far as bags go, saddlebags offer quite a bit of storage as well as a tail/tank bag. I opted for a Cortech magnetic tank bag so it can be easily removed and used on another bike. Some expand to hold nearly as much as saddle bag and have nearly waterproof covers to keep stuff dry.
Honestly & imho, most bike storage problems are addressed by being a bit on the creative side and increasing your packing skills to maximize what room you have available. For example; I can fit 3 xl hoodies in my Cortech Super Mini tank bag. But to be 100% honest too... I had to get my wife to teach me how to fold them.
