Athletes have used heat for recovery for as long as there have been athletes, and the reasoning is simple. Warm muscles get more blood, and more blood helps them recover.
What the evidence supports is modest but real. A session after training eases the tension that follows hard work, and most people sleep better for it. What it will not do is replace the training or burn meaningful fat.
Timing is the question that comes up most. Go afterwards rather than before, unless you are deliberately heat training for an event, because a sauna before lifting leaves you flat. The guides below cover saunas around workouts and how heat compares with cold water.