I totally support Markus opinion to avoid WiFi in battery powered devices. WiFi is a really energy hungry technology, not suitable for devices that are powered by batteries.
As for your questeion about bluetooth: In my understanding buetooth is a near-field technology. It might be possible to use when you have a bluetooth controller/sender in every room. If you want to control thermostats deployed over several rooms, other radio technologies are better suited.
I suggest to look for radio controlled thermostats that are available in your country and then decide which technology suits your usecase best.
In my case I decided to use Z-WAVE for different actors/sensors. My thermostats are “Eurotronic Spirit Z-Wave Plus”. The usual disadvantage for batterie driven devices in Z-Wave (they need to “wake up” to receive commands, which can take a few minutes) is eliminated by the FLiRS technology (Frequently Listening Receiver Slave). These thermostats react nearly instantly to commands. I am very satisfied with their performance and a set of batteries lasts around 1.5 years in my setup. You would need a Z-Wave controller to connect them to OH. I do not know if these thermostats are available with alternative radio technology.