In my case, about 1.5 years. There are two AA batteries. Changing them is easy, yes.

In my experience, the battery lasts about a year. In my opinion, it only makes sense with rechargeable batteries (but there again, the battery status determined in the app is unusable because of the different performance characteristics).
Two AA batteries are needed (included). Changing them is a bit fiddly, but you can do it without tools.

All in all, you can be prepared to make a tour of the flat once a year and change all the batteries. For me, with 8 thermostats, this takes about 15 minutes.