Best time of year to go?
My suggestion: Go and check it out! Bearing in mind that optimum temperature is subjective, there will always be some who'd like it hotter. I haven't visited the private pools but in the communal Desert Pete area, water temperatures vary a bit between the various tubs. I'd guess (based on my experience with my own hot tub) that the warmest Desert Pete tubs are ~102F and the coolest maybe 97-98F. Note: some folks like to take breaks from soaking by laying out on lounge chairs, so if that's your cup of tea, you likely should to go on a warm day rather than a cool one.
* Edit: corrected one misspelling of "Desert Pete"
I'd be thinking that with those water temperatures, anytime of the year in Arizona might be okay. My only encounter with hit springs was a cool Victorian winter evening (perhaps 10...15 C; in the 50s F) at Mornington Peninsula Hot Springs and I was fine wandering from pool to pool in just my swim brief (they don't allow less). The supplied robe mostly stayed under my arm between pools.
(In hindsight, perhaps I could have worn the robe between pools and not the swimsuit! :-D )