Well, I'm not a climber, but I do scramble over the peak tops and canyons a lot.
The answer depends a lot on the luck of the draw. For example, Sunday it was 80F in Vegas; Monday it was 65F. I've seen days in June when the high at the RR Visitor center was 71F.
There are many climbs on N-facing walls. Much of the "heat" of southern Nevada is diminished if you stay out of the sun. Ice Box Canyon is so-named for a reason.
If you come out here and the temps are intolerable that week, you might consider climbing at the Hood off Kyle Canyon -- starts at ~8000'.