Whats the ambient temperature and humidity in your town?
Leaving the door open mostly solved my problem here as well.
Using the Sauna, I was told that it was important to do a quick spray of warm water over the soles of your feet at the very end of the shower. Reason given: there are warmth receptors on the sole of your feet. If you just pour hot water over your Body, your Body thinks you are overheating, and starts sweating to cool you down, which continues after you turn the shower off (also why a cold shower in summer is not as refreshing as a lukewarm: the latter just rinses off the sweat and cools with Evaporation, the former messes again with your body’s Thermostat).
If you pour warm (not hot) water over the receptors, you trick your Body into accepting that you are warm, not hot, and no Change in metabolism = sweating is necessary.
I don’t have medical evidence or cites for this, just that it works for me.