Well, you are in the middle of Japan's rainy season.
Nah, the rainy season's pretty much finished now, I think. I get the impression these thunderstorms are just a normal part of summer here (plus the occasional typhoon). It was raining a lot more a few weeks ago. I miss that rain, it lasted a lot longer, so it really helped cool things down a bit 
Now imagine being among the Japanese who wear suit to work everyday. How do they even survive :S
Commuting isn't actually too bad, provided you can avoid going outside too much. Even when you're crammed into a subway train like sardines, it's still a lot cooler than it is outside, and almost all indoor areas are air conditioned to some extent (on the other hand, once I get off the subway, I have a 20 minute walk up a steep hill to get to uni. Not fun).
It's also considered fairly acceptable to not wear a jacket to work at this time of year in a lot of places. The government launched an initiative a few years ago called "Cool Biz" to try and make this standard practice in all Japanese companies, with moderate success. On top of that, with all the nuclear reactors switched off, there's a real problem with energy shortages during the summer, when everyone's using the air con, so a lot of companies feel they have to do their part and get employees to dress lighter, so they can turn the air con down a bit and save electricity.
One company even went as far as making its employees, all several thousand of them, get the same identical haircut, which the bosses have decided is the most efficient haircut for keeping your head cool.
