How can a north facing wall be hot? It can't. A true north facing wall is in shade all day and all year for most of the northern hemisphere. Is there some pavement that reflects light and heat? Is this wall perhaps northwest facing?

The type of shade along a north facing wall is essentially medium as long as the area has no overhanging tree. Medium shade is found under mature trees with high limbs and open canopies. Many plants will do well, including daylily, fuchsia, impatiens, wood anemone and oak leaf hydrangea. Granted, most of these plants are not grown in Arizona. Plants that will grow in deeper shade will bloom better with the increased light of this area, but since they won't actually be in sunlight they can't get scorched. The only plant that comes to mind is Prunella grandiflora which will tolerate sun to shade and dry soil.

There are many species and cultivars of Ruellia, and most will take shade or sun. Most Lantana likes sun. L. montevidiensis will take part shade. Both Ruelia and Lantana will take heat and (once established) drier soil. The more I consider this the more I think the issue is about dry soil. I recommend you visit a local nursery (not a big box store) and ask about plants that grow in dry shade. They can advise what does well in your local climate and soil.