This isn't a thermal option, but the iron-air chemistry has promise too. It's basically rusting and de-rusting iron. Much more environmentally benign than lithium ion, and likely way less expensive. AFAIK, this company is the frontrunner: https://formenergy.com/technology/battery-technology/
Iron-air are just another kind of metal-air batteries. The problem with all of them is that hydrogen-air batteries have existed for decades and is basically the same thing. If it wasn't for 20 years of marketing propaganda we'd realize this and never bothered with reinvesting the wheel with another chemistry.
I hear you that marketing spin is a factor here. But if Form Energy can achieve the $20/kWh price that they're pursuing... iron-air is quite different from other chemistries on the financial front.
https://www.utilitydive.com/news/form-energys-20kwh-100-hour...
(I have no affiliation with this company.)
By hydrogen-air battery do you just mean a water electrolyzer system paired with some kind of hydrogen fuel cell?
If so, the metal-air systems have a major advantage on the discharging side of things by avoiding the need of a fuel cell and being able to harvest electrons directly via galvanic current.
A hydrogen system is basically the two sides of a battery split into separate components. It's fully possible to build device that does both, although as of today this is less efficient.
The galvanic discharge rate is extremely slow and not really suitable as part of a rechargeable battery system. Any practical metal-air will have some way of discharging faster. The problem is that we have basically solved this for hydrogen-air but not for anything else.
This isn't a thermal option, but the iron-air chemistry has promise too. It's basically rusting and de-rusting iron. Much more environmentally benign than lithium ion, and likely way less expensive. AFAIK, this company is the frontrunner: https://formenergy.com/technology/battery-technology/