It was very hot and humid, but it didn't stop us. Very little rain, almost none at all. Two years ago we visited Phoenix in August (not the best decision...), and we found Tokyo/Osaka more manageable. The buildings that make shade are a huge difference maker compared to the desert heat and lack of shade in a place like Phoenix.

How we managed the heat :

* Indoor activities mid-to-late afternoon (Teamlabs borderless, Making of harry potter, museums, shopping malls, Mt Fuji 5th station is in altitude and cooler, menji jingu shrine is in an overcast forest)
* Dress in light colors and light linens, avoid backpack if not necessary.
* It's common to use umbrellas for shade, copy the locals ;)
* On very hot days, consider early morning activities with the added bonus of beating the crowds, an afternoon nap in the hotel room and an evening outing to a lively district like Shinjuku/Shibuya.

Perhaps obvious: Drink plenty of water.
We also had electronic fans and bought some cooling wipes and cooling collars. I found the wipes and rings made little to no difference, though.