[...] I thought you would be a great person to ask about Paris in the heat. My wife and I will arrive this coming Wednesday, and it appears that it is going to be extremely hot this coming week. Do you have any tips, or place to go for a little refuge from the heat?
The apartment we rented on Île Saint-Louis is not air conditioned, and we’re getting a little concered about the full enjoyment of our trip. Any advice you can give me as far as restaurants, museums, bar, or anything else would be greatly appreciated. [...]
Great question! The French really don't do AC for the most part. It can be brutal on those unusually hot summer days, which only come every few years. Fortunately most summers in Paris never got as hot as NYC (where I am now), but it sounds like you've hit one of the unusually hot weeks. I'm not surprised your apartment doesn't have AC; I don't think I've ever been in a Parisian apartment that does. If they don't have a fan, you might want to consider buying one as soon as you get there. Darty or Monoprix are two good places to buy one. BHV is a good option too, and pretty close to where you're staying, but probably the most expensive of the three.
This might sound silly, but my number one tip for wandering around Paris on a very hot day is popping into every supermarket you see and cooling off for five minutes. It's the one place that's guaranteed to be nice and cool inside (or, at the very least, the dairy aisle is). Keep an eye out for supermarket chains like G-20, Champion, Franprix, and Leader Price. Also, Monoprix is a big store that's all over the place, and some of them have a supermarket inside, while others don't. Worth a shot.
Beware, a lot of snack and fast food places have bottled drinks in a refrigerator thing, but they're barely cold! The French just don't do unnaturally cold the way we Americans do. Make sure to touch and see if a drink is cold enough for you before you buy it. Supermarkets are a better bet for this. (And you can't go wrong with a beer at a café; that'll be nice and cold.) I'm sure you've heard the stereotype that French restaurants don't have ice cubes, and this is usually true.
A lot of restaurants have a sign on the window that says "salle climatisée," meaning air-conditioned dining room. These are often not true! If you want to confirm before being seated, I do this trick all the time where I go into a restaurant alone and pretend I'm looking for someone. "Bonjour. Je cherche ma famille." ("je shersh ma fa-mee"; I'm looking for my family.) I usually do this just to see if a place is noisy/crowded/terrible, but it'd work for checking for AC as well.
I suspect most museums do not have air conditioning. And even movie theaters are often not air-conditioned! Or they've only got the AC on a tiny bit; they're never cold like in the US. They're often downright hot inside if the weather outside is hot.
Île Saint-Louis is a fantastic place to stay! I'm jealous! The island is tiny but there are two great gelato places there that might help you cool off. My favorite is Bertillon, and my fiancée's favorite is Amorino (Amorino is actually a chain with many locations around Paris).
It just occurred to me, I'm sure the catacombs are nice and cool this time of year!
One nice thing about hot weather in Paris, it almost always cools off a lot at night. So whereas we get nasty hot humid nights in many parts of the US, Paris usually gets much cooler, even to the point where you'd want long sleeves at night. I can't promise it'll definitely cool off at night, but I hope this is the case for your stay!
I hope some of that helps! Good luck and have a great trip!