In reply to Shone: Agreeing with the others, JTree will be way too hot in August. In an old US climbing mag Randy Leavitt (I think it was) wrote an article about summertime climbing there---pre-dawn alpine starts, almost stepping on rattlers out hunting (and hard to distinguish by headlamp light) and only getting in a single pitch at first light. However there are other alternatives in the area. Tahquitz Rock is not far and at much higher elevation. The walk up will be hot, but once up there shady, cool climbs will be available. There are also bouldering areas around Idylwild. The Needles and various other domes and formations in the southern Sierra will also be tolerable and aren't "too" far from JTree.
As Peak DJ said (Hi, Dave)Arizona can be fine in summer if you pick your location. As he mentioned, the Flagstaff area is at a high enough elevation that climbing in the summer shade at the various areas accessible from town is quite reasonable.The Pit (limestone) isn't the greatest crag by any means but has some good routes, but the basalt cracks of Paradise Forks are well-worthwhile, though very demanding. There are other areas as well. Jacks Canyon is across the state and fairly controversial in the States (a number of chipped routes) but, as Peak says,does have a good collection of routes and some sectors will be in the shade at most times of the day. Both these areas are in northern Arizona. I'd skip the Prescott area in August. Granite Mountain is a superb crag but gets sun most of the day, so I imagine that it will be broiling there during August, while the other local crags are also likely to be hot, and not really worth the trip. However in southern Arizona, Mt. Lemmon above Tucson has crags at various altitudes all the way to the end of the road at around 10,000 ft. In fact the highest crags have probably the best rock on the mountain, are well worth visiting, and are often very pleasant while the temps in the city below are well above the "century" mark.(Though in August you will be in "monsoon season" in that area with the likelihood of relatively brief, but torrential downpours, so keep an eye out on the weather) So with a bit of planning and traveling climbing is possible in both states even in the hottest months of the year.