Last week up through Saturday was quite a bit worse. Temp was up to 36C. There's definitely a body type / tolerance thing, because my wife doesn't mind the Tokyo humidity at all. I, on the other hand, hate the humidity, even though I love the dry heat and loved AZ summers.
Yeah just try to stay indoors. I could entertain myself all day long in Shinjuku or even Ikebukuro without ever taking a step outside. It helps if your hotel is directly adjoined to shopping/dining complex and train station.
Depending on the train station, there may be a department store adjoined to the concourse. So if you've got some spare time to kill while waiting for your train, you could go into the air-conditioned department store to wait it out and minimize the time spent waiting out on the muggy platform (although trains like Yamanote come every 2 minutes anyways).