My own experience (n=1).
I trained for a few years without a fan. At first I had a cooler place in veranda (could be 13°C in winter) without any negative effect from lack of fan. But last few years I had a smaller room which heated up during a 60 minute workout. It was harder to do the workouts but sill manageable. I left a puddle of sweat after each workout and my heart rate crept up as intervals went by.
It got too hard as I approached 4 W/kg. I found this deal for a carpet dryer on forum and it was a great choice.
The only issue I experienced was catching cold after a few sessions. You should keep you paincave clean from dust and position your fans to not blow in your face.