Some of this discussion may help you out.
http://www.bikepacking.net/forum/index.php/topic,3936.0/topicseen.htmlIt can still be hot down here in the South that time of year but the sun is less intense for sure and nights cool off better.
Can you make it late Sept to mid Oct?
Also be sure to note the N-S recommended route change on Mt Lemmon. Up the Control Road not Oracle Ridge Trail then down whats called the Lemmon Drop Trails instead of pavement.
Tim