On Tue, 07 Feb 2017 11:11:17 -0800, wrote:

If the thermostat only turned the furnace on and off I could see
battery power because there would be only two wires. But my thermostst
will and does control much more and there are several wires connected
to it. Not only that, my house is only 8 years old so the furnace is a
modern one. A memory backup battery I can understand but my thermostat
uses the barreries to power the complete thermostat, even powering
the mechanical relay. And anyway, either the memory is non-volatile or
there is a super capacitor on board because the memory is not lost
when the batteries are replaced.
Eric

When I changed the batteries for a second time yesterday, the digital
numbers were still there after I removed the batteries, but by the time
I opened the batt package they faded away.

I just have 2 wires. I had a new furnace installed this last Novemnber.
It still only has 2 wires. The guy never even touched the thermostat.