I don't do well in heat, and Kyoto has to be one of the worst places in the world for it. As Japanese people invariably say when you mention Kyoto heat, Bonchi da kara ("That's because it's in a basin.") I once spent two summer weeks in Kyoto, and when I returned to Tokyo for a day before flying home (many years before KIX), Tokyo actually felt COOL, something I never could have imagined before.
Surrounded by mountains on three sides, Kyoto has high humidity and no discernible air movement. The statement, "It's not the heat; it's the humidity" is very true here.
Two hazards are:
1. Heat exhaustion: If your head starts to hurt and you feel nauseated, find an air conditioned coffee shop or restaurant immediately and drink lots of liquids. (Cola drinks are good for nausea.) If feasible, go back to your hotel, drink some more liquids, and lie down in the air conditioning.
2. Shoe sores, known as kutsuzure in Japanese. The heat will make you want to wear sandals, but the least bit of friction will cause painful chafing. Either wear socks or put large, flexible fabric bandages on the painful spots.
But don't let these warnings put you off Kyoto. It's a great city, especially if you go off the beaten track and explore the little side streets.
Oh, and if you're just mildly overheated and thirsty, Kyoto has great beer gardens along the Kamo River.