According to an embodiment, an electrode system for a burner may include a thermally coupled electrode configured to apply an electric field to a region corresponding to a flame or combustion gas produced by the flame and to receive heat from the flame or the combustion gas. A cooling apparatus may be operatively coupled to the thermally coupled electrode and configured to remove the heat received by the electrode from the flame or the combustion gas. According to another embodiment, a method of cooling an electrode subject to heating by a flame or a combustion gas produced by the flame may include applying an electric field to a flame or combustion gas produced by the flame with an electrode.