I've worked out while on the cleanse but I found that it made me feel too worn out, like I didn't have enough steam to really enjoy my workout. (I use a stair-stepper and some hand-held weights).
My speculation is that doing a workout while on the cleanse isn't the best idea because you don't have a whole lot of extra calories to burn.
As for the steam room, I don't know. I wonder if anyone else has any answers on here? Personally, I'd just take it carefully. I'd go in the steam room cautiously, getting out if I started to feel light-headed or anything.