Sorry to crash this as an American, but we have months of 45°C temperatures here in Texas with a really humid climate, so I might be able to offer some advice.
One summer my AC was out entirely for about a month. I survived by positively soaking a sleeveless tank in ice water and sitting around in that until it wasn't cooling me anymore and then soaking it again.
I recently found some ice packs that go around the neck, and they really work miracles for lowering one's body temperature. I always keep one in the freezer now for when I get back from a walk.