Of course it's hot!
Tokyo is at the same latitude as Kabul, Casablanca, and Florida...
Look at a map or better, draw a horizontal line from East to West, at the level of Tokyo. What happens? You will notice that well, Tokyo, and even more Kyoto, are quite South. As South as Kabul, Beirouth, Sfax, Casablanca and Jacksonville, Austin ...
And Japan, is an island, all surrounded by water! So you get both heat and humidity in Tokyo and anywhere else besides The Northern part.
What do you do to get used to the heat? Well, my advise is to avoid as much as possible air conditioned places and to get your ambitions down to live slowly.
If you want your body to adjust to the heat, and make your life cooler, avoid air conditioning. Artificially cooled down air will make heat feel worst, and will give you thermal shocks that are very bad for your health, especially if you have some blood pressure problems. You could also get a bad cold. So, not good.
The best thing is to stay outside as much has possible and enjoy. ideas:
Go to Mitaka and Takao mountain:
There is the Ghibli museum in Mitaka. It is very nice and poetic and you could spend half a day there enjoying the imaginary world of Miyazaki.
Then, you can take the chuo line and go to Takao mountain (a small one) and enjoy the treck up its top. On the way down, there are a few onset - hot spring to enjoy too!
Another idea is to visit Kamakura. Don't forget your bathing suit. Visit the Great Buddha and then, you can change in any combini store along the shore, spend 2 or 3 hours bathing in the sun and watching people, visit Enoshima, get to the spa there and refresh before enjoying diner on the seashore many restaurants surrounding Enoshima. Shirasu (steamed baby fishes) are the speciality there; try the shirasu-don (shirasu on rice bowl).
If you avoid the heavily urbanized places, you will be able to enjoy the heat, even Odaiba is nice!
Around Kyoto, to stay out of the city, you can visit either Mount Hiei up North, or Adashino Shrine, North-West, of the city or Fushimi Shrine, down South. Katsura Imperial Villa is on the way. You need to get an authorization beforehand. http://sankan.kunaicho.go.jp/english/guide/katsura.html
In the evening, a diner in a terrace or a rooftop beer-garden along Kamo river will make you day end in a lovely and cool way.
Anywhere, you can find nice little cafés to take a rest, and, hydrate. Very important. Oh, and don't forget to buy yourself a watermelon cut at a supermarket.
So you see, with appropriate clothes (lots of T-shirts and shorts, beach sandals, and don't forget the little towel that the Japanese use to dry their hands but that you can use to clean your sweat away), the wish to enjoy your visits in a slow mood, you can enjoy Japanese heat!