My thermostat runs on batteries but it has an LCD, similar to (http://smile.amazon.com/Honeywell-RTH2300B1012-5-2-Programmable-Thermostat/dp/B007BHLUWM/ref=sr_1_1?ie=UTF8&qid=1425045609&sr=8-1&keywords=thermostat) but I thought any type of display (LCD) would suck up the battery. Am I missing something, is this a special type of display?
LCDs (liquid crystal displays) require very little power to operate. The liquid crystal looks mostly like a small capacitor. To keep the liquid crystal in the dark state, a few volts of AC at a few kHz or so must be applied across this capacitor. That's not a lot of power.
This is exactly why you see LCD readouts and displays in low power battery operated devices to often. Think of a wristwatch. Those run for a year or more on a tiny battery.