What type of battery does a house thermostat use?

That's like asking what type of tire does a car use.

You have to look and see which ones and how many YOURS uses. And pruchase accordingly. They aren't all identical.

I could tell you what size mine uses...but yours might be different. As an example the last two I've had in my house used different numbers of batteries, but the same size.

Open the front and look. Typically they use an AA battery but some don't