It strikes me that the logical thing might be something that attaches itself to the brickwork with holdfasts. I'm not sure what plants fit that description in your climate and how concerned you'd be about having a plant growing directly on the wall. To keep the heat out of the room, the best thing is blinds or curtains kept closed in the heat of the day. How wide is the side yard? Can you plant a tree or hedge along there to shade the wall?

You might try a crossvine (not trumpet vine) and see how you like it. You can get modern varieties with Rose or Orange color. It should remain evergreen in your area and it has little grips that will suction to the brick, yet it is not structually invasive. It will pull away easily should you desire to remove it later on. It is fast growing, especially if you provide good quality soil in the planting hole. Beautiful blooms mid to late April that the hummers adore.

I planted two varieties last summer, one a native and one called 'Dragon Lady' which has a deep rose bloom and am extremely pleased with their performance. Dragon Lady is covered with buds and I noticed the first one opening this morning. The native crossvine produces fewer buds but has a lovely bloom of yellow w/rose colored throat.

Another good vine is the climbing hydrangea but I'm not certain how invasive the little grippers might be on brick and it is slow to get started. It isn't evergreen but does have lovely clear yellow fall color and interesting bark. You might also want the wall to be bare during winter days, so the sun could heat the brick.

The only drawback with using vines in your situation is who will trim them when they reach the roof line?

Mary