Some people have fasted with sauna use. Some fasting doctors even advocate it, so it seems like here is another contraversial subject. My advice would be that if you used the sauna during your fast to do it carefully and record how it effects you each time you use it and for the next day after, noticing any good or bad effects. I would never use the sauna while tired during a fast, I would consider that dangerous. However I would exercise at times while tired to the point of sweating, it's using the body's own processes to stimulate the sweating whereas the sauna makes you sweat whether you are up for it or not.
So be careful, you may want to start slowly but don't give up on the idea completely until you've at least researched it a lot more.