You don't even need an expensive AC. If you can't afford one, you can just get an evaporative cooler[1] for $100 or lesser[2]. Possibly even cheaper if you don't mind buying a second-hand unit.
The main reason high heat causes issues in Europe is due to the high humidity, so you can't get rid of body heat as your sweat won't evaporate. It's why 35C in the shade might be perfectly fine in Nevada but absolute hell in the UK.
For exactly the same reason an evaporative cooler isn't going to work: there's no "space" in the air for the water to evaporate into.