Yep, that is why I have at least two baths per week, between 2 and 6pm, at a temp of 40 degrees C per a pilot trial on hyperthermic baths as treatment for depression. I’ve been doing it for a while, with definite sleep benefits. I’d say I’ve sometimes not really managed much beyond the spirit of it (my bath is a bit too small for full-body immersion), so I’m curious how it’d be if I had access to a deeper tub. On the other hand, reading in the bath would be more difficult then!
It’s hard to say how well it’s helped my anxiety because external-to-my-brain-chemistry causes made it spike over the last six months, but I’d say it’s had an impact there too.