My take is that your heart and lungs are working out, even if your body is not. Do you get the same benefits as going for a run or bike ride for a comparable amount of time? no, since your limbs don't get fit, but your heart and lungs do.
Please ignore my comment, though I will leave it to make the below comments less confusing.
Original: You don't want to "work out" your heart though. Cardiac hypertrophy is a bad thing.
The benefit of exercise is that your muscles become more oxygen-efficient. Your heart endures some stress now, so that it can work less in the future.
Eccentric hypertrophy (athlete's heart) is the positive adaptation resulting from training the heart. The heart has a lower resting rate and is more efficient at pumping blood. It returns to normal size if training stops.
You'll never reach a state of hypertrophic cardiomyopathy (the bad kind of hypertrophy) with exercise. Its cause is usually genetic.
That additional oxygen needs to come from somewhere. Endurance training at the same time trains the heart to deliver more oxygen to the periphery; the primary mechanism is increased cardiac stroke volume.
Cardiac hypertrophy isn't a "bad thing". This is completely contextual. What you don't want, for example, is pathological hypertrophy from things like hypertension, or exclusive left ventricular hypertrophy without associated increase in chamber size.
The heart is very complex. You 100% should exercise it.
Afaict, the grand parent poster is just very wrong. You do want to cause acute stresses to your heart (cardiovascular exercise) to get it work better.
Sources?
(attributed to Bertolt Brecht)
Endurance athletes obsessively track VO2 max, basically your body's ability to consume oxygen during workouts, and it certainly doesn't improve with sauna training.
It's like asking "if you only did puzzles, would you be smarter?" Well, in a way, yes, but if you actually want to compete with someone with a good education you have to read.
Same with physical exercise. It puts a lot of different stresses on your body that saunas don't. The question isn't "do saunas make you physically fit," because they don't. The question is "for people who don't want to exercise, does sauna training alone meaningfully extend your healthspan?" I'm guessing the answer is "a little but not enough," but I'm not sure.
Yucatan is not the same as Dubai in Summer.
Your body is under heat shock trying to keep up in a Sauna (that isn't considered warm until 60°). Versus a healthy body CAN keep up in 40°.
The Yucatan equivalent of a Sauna is more like doing hard labor on a roof on a sunny day with no breeze.
If heat training is better than another interval session remains to be seen but it seems a lot of smart people believe it's worth it nowadays.