As tokyo friend said, sunshades and hats! Make sure the hats are a light weave and breathable. That goes for your clothes too. Choose fabrics that will breathe. Also, don't forget the sunblock!
Japan has lots of stuff to help deal with the heat. You can buy bandannas that you stick in the fridge or freezer and then wear around your neck (this works for anything actually, just wet some cloth, stick it somewhere cool or in front of a fan, then place it on your neck), but the ones they sell in combini/stores are usually a gel, which can last longer.
Regular fans are sold everywhere, either the uchiwa or sensu styles. Grab one of those, or spring for the fancy spray-bottle and fan types that mist your face.
Anytime you start to feel too hot, drop into a combini. Not only are they always air conditioned, but they sell bottles of ice or frozen drinks, and are a good break in between hot walks. Even if you go in to browse, combini are there to help you get out of the heat, so don't feel bad for stopping in a bunch! Same with other public spaces, stores, department stores, restaurants, etc. It is better to stop and rest a bit than get heat stroke!
And know the signs of heat stroke/heat exhaustion and what to do if it happens, or you start to feel bad (or your parents). Don't wait, and don't try to push! Get them somewhere cool immediately.
Try to do things in the morning and evenings, and save the hottest part of the day for inside stuff... museums, castles, lunch, etc. Also, don't underestimate the power of nature... it often drops several degrees around trees, rivers, streams, etc. Go for leaf cover and some nice nature if the concrete of the city gets to be too much! Even a park will do!
And don't worry too much... take it slow at first, but they should get used to the heat a bit. It's still a difficult time to travel if you aren't used to it, but they will have fun regardless of the season!
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