This is why you might want to consider getting an air conditioner. You won't need it most of the time or sometimes even for a year. But Europe seems to be getting more of these heat waves (think France) and even if you only use it for a few days a year, it could make your life much easier. They're like first aid kits. You may rarely need it, but when you do, it's essential.
Otherwise, I suggest opening your bedroom windows at night then setting your alarm for just before dawn. At that point close your windows and pull your curtains and draw your shades. Make your room as dark as possible and keep the door closed. This will help keep your room cooler than the rest of the environment by a few degrees. If you have sheer curtains then get some blankets and use them to insulate the windows. Dark and cool is good. A north or east-facing room is cooler than others and a room with cross ventilation is better than one with none.
I do feel sorry for you guys. Dealing with heat when you're not used to it is awful. I know when I go down south it can take up to a week to acclimate to the temperature/humidity difference and that's one miserable week! It's much easier to gradually adjust to it with seasonal change as we usually get to do here in the states.
Just take it slow and rely on cool fruity drinks. If you're making lime, lemon, or orange ade (citrus is great for this), add sugar as it helps with quickly processing the citrus juices. Heavy sweating depletes your salt content so a really nice thing to do is to rim your glass with lime or lemon and then dip the glass in kosher (and only kosher!) salt like with a margarita. That will give you a really great glass of limeade or lemonade. And do use a lot of ice. I know you people have a thing about iced drinks but do it like we do when it's very hot out.
Oh! And yes!! Do wear an all-cotton T-shirt under another shirt even if it's just a T-shirt. You will actually stay cooler. Same thing with bedtime. Keep a cotton sheet on your bed and then direct the fan on to that and you. You'll sleep cooler. The only time you want to not wear a T-shirt is if you have linen clothing. Linen has the unique property of absorbing moisture and is the only material that's stronger wet than when dry. Linen fibers are hollow and they will take-up your perspiration and help keep you cool by releasing that moisture, creating an evaporative effect. This is why wearing linen in the heat is so popular. Just be sure to keep drinking. You'll know you're hydrated when you pee clear urine (again though, be sure not to rely exclusively on water).
