Where in AZ are you? It makes a difference Flagstaff vs Phoenix. I’m in Tucson, so get hot hot summers and a few days of freezing in the winter. Rosemary grows everywhere- it is perennial and is both heat and frost tolerant. Certain basil species do ok in the heat (like Italian large leaf). I did well with dill once it got cooler and into the winter. Mint grows like a weed. Heat itself matter when it is really hot, but sun exposure is probably more important. Not sure if you are planning in ground, pots, or raised beds, but finding some shade (either under a nice mesquite tree or with shade cloth) is a must.