Heat safety is a critical concern for group fitness classes — especially for populations that don’t tolerate heat as well, such as older adults, people with chronic conditions, and children. But even younger, healthy adults can suffer heat injuries from exercising in temperatures that are too high.
The ideal room temperature depends on the type of class you’re teaching; 68-72° F is generally recommended for cardiovascular and strength activities. The cooler end of the range — or even a degree or two cooler — will be more comfortable for higher-intensity classes like Zumba® or cycling, especially with a larger class; for lower-intensity classes like yoga or mat pilates slightly warmer temperatures will be more comfortable.
Even if the room temperature is within an acceptable range, it’s going to feel hotter as the humidity rises —via open windows, sweaty bodies, and increased breathing rates.
It sounds like you’re doing the best you can, given the circumstances. Circulating air is enormously helpful for mid-workout cooling; ask if management will equip the room with more fans, or a window-mounted air conditioning unit if central A/C isn’t an option. For safety, educate your participants about preventing heat illness, and make sure they take plenty of water breaks; dial down the intensity when the temperature starts to climb. You may also need to limit class size to keep the room cooler.