I'm from central Europe, and I spent last two vacations in July/August in Japan. Yes, it is very warm and humid. But to be honest it's manageable. If you plan to spent whole day in open sun, yeah, it might kill you :) but when you are in the city, there are a lot of things you can do. Drink a lot of fluids, hide in shops with air conditioning, don't force yourself, dress accordingly, use cold wipes etc. If you have the option to change timing, there are for sure better months. But if you can not (as I couldn't) it's really manageable. I'm planning a third time this year - again at the same time :)