I am wondering if I need to turn off my electric power in order to replace the batteries on my wall thermostat. If I do need to turn it off, should I turn off the main power on my circuit breaker box or just the circuit to my furnace ?

Thank you for your assistance.

While the control voltage for most heating and cooling systems is only 24 volts, hard to tell exactly what voltage you actually have, as there are some line voltage control systems. In any case, no matter what the voltage is, the power should be turned off just to prevent any problems. Even working on low voltage control can be a problem if the wrong wires are shorted, which can blow control fuses, or even damage the electronic thermostat.

Better to be safe than sorry.