Yes, if by hot bath you mean submerging yourself to neck level in 40ºC or above water for 20-30 minutes. There's no reason to believe any "heat therapy" modality is superior to another as long as you suffer equal heat stress.
For the record, if you're not acclimated, intense heat exposure is a lot more agonising than 30 minutes of exercise for less benefit. If you haven't experienced a properly tuned sauna in your life you are in for a ride. What's being studied in the literature is nothing like your standard hotel experience.
How are you suffering equal heat stress from being submerged in moderately warm water and breathing very hot air? I could imagine quite different effects on airways and skin, for example. "Exactly the same effect" seems like the unexpected outcome here.
> intense heat exposure is a lot more agonising than 30 minutes of exercise for less benefit
Having to do absolutely nothing other than not leaving is quite different from pushing through a physical activity that can also easily be causing all kinds of discomfort.
The standard hotel experience is sitting wrapped in a towel and longing for my winter coat! Actually I would probably feel similarly in this study, 73°c is really cold for sauna. 90°c-100°c is the sweet spot