I have lived in Arizona half of my life and storing your collection in a garage or attic space is going to destroy part of your collection. Just a couple of things I have seen over the years; cards drying out and breaking up (older vintage cards), cards with coating sticking together, binder sheets drying out and becoming brittle, penny sleeves turning yellow, autographs disappearing on balls and cards and cards either getting jaundice (turning yellow for base type cards) or Hulking out (turning green for older chrome/refractors).
I grew up in Tucson but I also lived in the Phoenix area and now live in Northern Arizona. Tucson isn't as bad temperature-wise as Phoenix but it is still bad at times. Additionally, during the monsoons there can be a sudden increase of humidity that can damage cards too if they are stored in an area without temperature control.