You should change your thermostat batteries on your programmable thermostat once a year. Most smart thermostats take alkaline batteries (AA or AAA) or 3 volt lithium batteries. These batteries 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.
On some furnaces, when the batteries get low they try to draw power through the furnace circuit and can cause a failure in the furnace control board circuitry. This is a costly repair, that can be avoided by keeping thermostat batteries fresh.
Some thermostats have a low battery indicator. This will emit a warning a few weeks before the batteries are dead. 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.