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Battery is a single AAA. I've had mine about 2 months and it is reporting 91% battery left with the unbranded cell it came with.
Range is okay but not great. One floor or one room away is fine but probably not much more.
For the DIY approach some of the sensors at pihome.eu look interesting and might have better range. https://www.pihome.eu/product/wireless-ds18b20-room-temperature-sensor-battery-powered-2/ - Needs a NRF24L01 receiver I think. The whole pihome system looks interesting, I hadn't seen it until this morning. Might order some and have a play.
How long does the battery last on that thing? And what is the range like?