What temp range are you looking at? The Gila is in the Chihuahuan desert (NM, far west TX) and along with the Great Basin deserts (UT, NV parts of ID, CO and boundary areas like northern AZ ) are classified as cold, high deserts vs. warm, low deserts in lower AZ and southern CA. (Source: Desert Ecology, 1990 printing)
Of course fronts and the winter jet stream can push some cold south in Baja...
If willing to drive to UT, maybe look at the Phoenix AZ area, namely "the Superstitions". Still can get below freezing even there. Specially reavis ranch (official) and "reavis falls" (unofficial trail) for a taste of everything ... desert, pines, riparian