Sauna After Glycolic Acid Peel?

I would wait at least 1-3  weeks following a chemical peel to go into a sauna depending on the depth of the peel and your skin type.

HI Glowskin. If the Chemical peels cause you some redness or irritation, it's probably best to stay away from the sauna for a few days. It also seems like weekly peels of this type are overkill. Daily Retin A or glycolic acid skincare programs can accomplish the same type of exfoliation at home and for much less $$.
Here's a different thought on the pigmentation. While we can't say without seeing a picture, we do know that Melasma is brought on by heat and even heavy exercise.
Many of our patients tell us that curling irons, saunas and humid summers cause their Melasma to worsen. You may want to get checked out regarding the potential for this condition as it may worsen with continued workouts in that hot yoga room.

I would avoid the sauna and heated yoga for at least 48 hours.  The heat from the sauna and heated yoga are not causing the brown spots.  Going out in the sun after doing the peels even with sunscreen can cause brown spots.

I'd wait 3 days to have a sauna after a chemical peel, and make sure to be very diligent with SPF 60 sunscreen for the week after a peel. The brown hyperpigmentation is most likely from the sun, not the sauna. You may also want to consider 50% peels every 2 weeks instead of 30% every week as far as results and cost.