It will be 97 degrees tomorrow in Vienna - quite hot for a place with very little AC.
Since we still have to get through July and August (and probably September) with hot temps, I thought it might be helpful to list some ideas for the heat.
Go Swimming - Visit Krapfenwaldbad, the swimming pool with the view (https://viennawurstelstand.com/location/krapfenwaldbad-outdoor-pools/), or the Schonbrunnerbad, located within the Schonbrunn Gardens where Franz Joseph learned to swim (https://www.schoenbrunnerbad.at/).
Eat Ice Cream - Obviously. Tichy Eissalon, iconic and kitsch, this place famously (in Vienna anyway) invented the Eis-Marillen-Knödel (apricot ice cream dumpling) - https://viennawurstelstand.com/location/tichy-best-ice-cream/. Gelateria La Romana, located off of the major shopping street of Mariahilferstrasse, is for certain the best gelato you can get in Austria - https://www.gelateriaromana.com/en/. I mean just have a look at their flavors - https://www.gelateriaromana.com/en/cat0_6657-the-tastes-of-tradition.php.
Visit a Museum - Nothing like a cool, dark museum to take your mind off the heat. To me, no museum is more iconic Vienna than the Upper Belvedere. Just be sure to arrive via Tram D next to the Palace, rather than entering at the Lower Belvedere entrance which requires an uphill walk in the full sun. Second to the Belvedere for me is the Leopold Museum, particularly the floors that focus on the Secession movement (Klimt, Otto Wagner, etc.). It is an Art Nouveau dream.
Go Underground - Very, very cool down here folks. The Capuchin Crypt is the final resting place of Habsburg royalty - https://www.wien.info/en/sightseeing/sights/imperial/burial-vault-341952. St. Stephan's Cathedral (Stephansdom) also has a cool crypt - https://www.stephanskirche.at/visitCatacombs.php. As a side note, with their thick stone walls and high ceilings, churches remain cool year round. As they are free to enter, step inside one of the many churches in Vienna for a quick cool down.
See a movie - Kind of a crazy idea when on vacation, but desperate times...There are two major English-only cinemas in Vienna, the Artis and the Haydn. The Artis is located in the First District, just off of Judenplatz, and the Haydn is on Mariahilferstrasse. Edit to add suggestion from hopper18 below - The Burg Kino, just across from the Opera House on the Ring. As noted below, they tend to show niche films, but also show the Third Man daily - which is a real treat to see in Vienna, followed by visits to filming locations.
Rent a boat - Head over to the Alte Donau, an old, closed off arm of the Danube and hire a motoboat (or a pedalboat, or a sailboat, or a boat that looks like an island complete with a palm tree). Jump in the water to cool off as needed, looking at the exceptionally charming boat and lake houses that fringe the water. Conveniently, the U1 subway line stops right on the water. I like to rent from Marina Hofbauer as it is right next to the U1 stop - https://www.marina-hofbauer.at/. If you want an island (super fun when you bring your own champagne and Trzesniewski sandwiches at sunset), go to https://www.meine-insel.at/. See here for sandwiches - https://www.trzesniewski.at/. There are also a few great restaurants at the Alte Donau - Das Boothaus, run by the famous Landtmann cafe folks - https://www.dasbootshaus.at/, Zur Alten Kaisermuhle - https://www.kaisermuehle.at/en/m and the Strandcafe, well known for their ribs - https://www.strandcafe-wien.at/essen-und-trinken
Stay cool everyone!