Fasting and the sauna do have their own benefits, but I do not think they combine very well: it would probably be best to avoid extreme heat (or cold) while fasting as this could prove to be very enervating for the fasting individual.
Most fasting authorities of the past recommended avoiding extremes of heat and cold for that very same reason; it could also lead to greater expenditure of energy and depletion of food reserves at a faster rate, when conservation of both would be preferable to allow the work of detoxification and healing to progress for a longer period of time.
Food for thought.