Yes, a thermostat issue can cause a furnace not to work. If the thermostat is malfunctioning or not set correctly, it may not signal the furnace to turn on or may not accurately regulate the temperature. Common problems include dead batteries, faulty wiring, or an incorrectly programmed thermostat. Regularly checking and addressing thermostat issues, such as recalibrating or replacing it when necessary, is essential to ensure proper communication with the furnace and maintain a functional heating system.