Why is Arizona the fastest-warming state in the U.S. (since 1970)?
The University of Arizona's South West Climate Network webpage Precipitation Changes  (Lenart, 2008) provides a detailed account of the causes of the warming in Arizona and the south-west region of the United States.  Principally, a major factor to consider is that the region is already arid, with low precipitation and high temperatures to begin with.

According to Lenart, global climate models predict that precipitation in the region is expected to drop in the region by between 5-10% by the end of the century.  Less rainfall, coupled with higher temperatures would cause an increase in dryness, hence droughts and sudden downpours.

The mechanism behind this precipitation drop is described by Lenart as being due to an increase in the area under the Hadley Cell circulation, resulting in a movement of the jet stream further north - resulting in winter storms bypassing the southwest altogether.  Some of the models predict there would be a northward shift of the subtropical anticyclone.

So how do these models match the observations?

Observations and measurements have found that


  lower precipitation rates in the Southwest correlated with positive phases of the atmospheric pattern known as the Northern Annular Mode (NAM), which they attributed to an associated northward shift of the jet stream during these years. Meanwhile, the Rocky Mountains, headwaters of the Colorado and Rio Grande rivers, tended to register higher precipitation rates during these positive phases, consistent with the observation that the jet stream was shifting north.


However, extreme precipitation events, such as the record breaking September, 2014 floods in Phoenix, as the remains of Hurricane Norbert swept through, are increasingly likely.  Crucially, from Lenart:


  Precipitation records contain a high degree of variability, however, as they are influenced by a variety of other factors in addition to climate change. For instance, much of the upward trend in the precipitation record from 1950 probably stemmed from an abundance of El Niño events in the second half of the record, according to Martin Hoerling, the researcher who conducted the analysis.


An interesting and somewhat ironic twist implied in the document The Heat Is On: U.S. Temperature Trends is a speculative point that


  points out that since cleanair
  regulations have dramatically reduced these
  emissions over the past 20-30 years, the cooling
  e"ect has already disappeared and will no longer
  be a factor in the future. If the study’s findings turn
  out to be applicable to the warming hole, then it
  is possible that without aerosols screening solar
  radiation these regions will catch up.


Anthropogenic sources, including land use can, according to the article Mesoscale Disturbance and Ecological Response to Decadal Climatic Variability in the
American Southwest (Swetnam and Betancourt, 1997), can amplify, mute or be utterly confounded by anthropogenic effects.