“I know GG of TM ”
do you mean the Grand Canyon of the Tuolumne? Well yes it will be very hot, but it climbs to somewhat cooler elevations soon enough. Of course, climbing in 90+ degree temps is difficult. Still, the route runs by a river, so water is available.
But why? Why not go to Tuolumne meadows and plan a hike that stays at cooler elevations? Unless you’ve already seen everything in the area and want to complete a list.
Sorry if I’ve misunderstood you, but you mention Pate valley so I assume you mean the grand canyon etc.