And yet, it didn't. The battery, while continuously on the furnace power, in fact dipped below the level at which the thermostat stops functioning and left the system turned off overnight. Their "low" threshold is 3.6 volts, and the thing drops off wifi if it dips below that, and stops working completely at some voltage below that (I don't know what that lower voltage is but it did dip below that too). What I did with the USB cable was to barely push it above 3.6 for long enough to get it to work again for a while.

But just now, I check it, and it's done it again despite the hack I applied yesterday.

Yeah, this thing needs a new battery.

Anyone know where I can get one?