The present invention is directed to a method of estimating an overheating temperature of an oil-immersed electric appliance in which ester oil is used as insulating oil. The overheating temperature is estimated based on a first concentration ratio representing a concentration ratio between two types of gas components contained in the ester oil and a second concentration ratio representing a concentration ratio between other two types of gas components contained in the ester oil. The first concentration ratio and the second concentration ratio are selected from a concentration ratio between acetylene and ethane, a concentration ratio between acetylene and hydrogen, a concentration ratio between acetylene and methane, and a concentration ratio between acetylene and ethylene.