This is a common belief. Some of my workout buddies believe
this.
From personal experience however, when I workout with AirCon (I
still perspire), my body is kept cool more quickly and effectively,
and I can workout more thoroughly. Without AirCon, because my body
gets too heated, and needs more time to cool down (to continue with
workout), time is wasted, and my workouts are not as
thorough.
For this reason, from personal experience, workouts with the AirCon
on, are much better... for me anyway. To each his own.