If the person sitting next to you in a sauna has it, that's plenty of time to catch it? Also, there isn't enough heat to kill it in the locker rooms or rest of the gym (where I have access to one.)
The gyms never closed here and they looked at the data. They found that gymgoers didn't catch covid in a higher degree than regular people during the pandemic, you should see if there exists a similar analysis for where you live.