The disclosed heater has a resistor (2) embedded in or tightly secured to a solid electrolyte (1). When an AC power source (4) is connected to the resistor (2), heat is generated both in the resistor (2) by alternating current, and in the solid electrolyte (1), because the resistor (2) heats the electrolyte (1), and increases its conductivity so that alternating current flows through the electrolyte (1) as well and heat is generated therein.