Different chemistries produce different voltages per cell. Alkaline produces 1.5v, NiMH produces 1.2v, Li-Ion produces 3.6v. These are averages, the actual voltage varies over the current charge level of the cell. This variation in voltage is how the low battery alarm actually works, although Alkaline cells produce 1.5v initially, once they are nearly empty they are producing 1.1-1.2v. Your thermostats will likely work fine on NiMH batteries, if you can live with them continually complaining about the batteries being low.
There are, or at least were, rechargeable alkaline batteries, but they don't last many cycles.
The 1.5v Li-Ions have a tiny circuit board on them that regulates the voltage down to 1.5v, which takes up space so the capacity is reduced. You could do that with NiMH, but it would have less capacity than the Li-Ion version, so there's little point.