@wonderwoman78 forecasts in remote places can be a challenge. Especially if you just google the name of a location, or enter a location in some random weather app.
Here on HAZ, when you look at a hike description page, there's an option to see the "trailhead forecast". This forecast is from the National Weather Service and does a reasonably good job at determining the forecast at that specific point.
Reavis 109 from the south (Rogers Trough) is shown here:
[ point forecast ]
Reavis 109 from the north (near Apache Lake) is shown here:
[ point forecast ]
You'll see on each of those that at the bottom it explains the location in miles from a recognizable named place, and the elevation.
109 north starts at 3500 feet, so it's considerably warmer. The trailhead forecast on HAZ is based on the starting point during the fire closure, which is no longer in effect. That forecast point is at 2398 feet ... which again is 2500 feet lower than Reavis Ranch, and subsequently much warmer. Confused yet? I understand!
109 south starts at 4800 feet, and the point forecast locks into 5213.
Reavis Ranch itself is around 4800 feet, so that's really what you want to know for your camping plans.
While it isn't a good indicator for rain or storms, when the weather is fair and calm across the state, you can use the forecast for other populated places at similar elevations. Payson is 5000 feet, and Prescott is 5400 feet. So the forecast temps in those towns will be pretty close to what you'll find at similar elevations elsewhere in the state.
If you hike from the north, the trailhead is by far the lowest (and thus, warmest) point on your hike. It has the same elevation as Globe, so that's a good place to check to see the likely warmest temps you'd encounter.
Of course all of this is imprecise. Especially a week out. It'll be more accurate in 3 or 4 days. You should also always be prepared for temps that are warmer or cooler than forecast. Things change, and to be safe you should prepare for some fluctuations.
I hate hiking in sun and heat ... but if it was me, I wouldn't think twice about backpacking to Reavis next weekend.
(FWIW, you mentioned Reavis
FALLS earlier ... that's a different spot, and while you can get there from Reavis Ranch, it's quite a trek and I wouldn't expect to see much more than a trickle right now, making the falls probably not worth the effort, IMO)