It's the high desert so typically fairly stable in late spring and summer - there aren't many storms and those that do occur are usually of short duration. We just don't get those multi-day or week-long storms that the NE is subject to.
However, it is the arid desert and it is the summer - the heat can be crippling. Never be surprised at high temps of 95 - 110 any time from June - mid September. Because of altitude, the sun intensity is also much greater than in the Gunks, therefore in the sun it can easily feel 10 - 20 degrees hotter.
So it can be very warm/hot but climbable or it can be unbearable. Usually though you'll have a good experience if you follow the shade and it's not abnormally hot. Depends a lot on your heat tolerance. It'll be in the mid-upper 90's for sure. Obviously June will probably be a little cooler than July. Bring hats and sunscreen. I also usually bring a big umbrella when I'm travelling in the desert in summer.
Another thing to remember is that unlike the NE, where the high for the day is often in early afternoon, here it occurs nearer the end of the day - 5, 6, maybe even 7 pm. IOW, if you're broiling at 2pm, the standard Gunks plan of waiting till 5pm to do the climb when it cools off probably won't work.
Finally, at that time of the year, there will be usable light to 9:30pm - 10pm since it's so far west but still in the mountain time zone. Idaho is an anomaly in that regard. The Pacific time zone starts on the UT/NV border but in ID it jumps far west to the ID/OR border - if it didn't, the eastern half of ID would be mountain and the western half pacific. Of course that doesn't explain why the ID pan-handle is Pacific and the bottom rectangle is Mountain, but time zones are wierd anyway.
Let me know if you need any other beta.