You should change the batteries on your programmable thermostat once a year. Most smart thermostats take alkaline batteries (AA or AAA) or 3 volt lithium batteries, all of which are commonly available.
Your thermostat has batteries to keep your programming saved when the power goes out. Even though your thermostat is wired directly to the furnace, a thermostat with a dead battery can lead to no heat.
Some thermostats have a low battery indicator, that will give you a warning a few weeks ahead. It’s good practice to change the batteries once a year, just like you would with your smoke detectors.
You don’t want to pay for an emergency no heat service call, just to find out your thermostat battery is dead.