Dielectric barrier discharge plasma actuators (DBDPAs) have been investigated for active flow control. The discharge induces ionic wind, which can be utilized for flow control; however, it simultaneously heats the flow and the dielectric surface. The thermal characteristics of the DBDPA must be clarified for applications in thermo-fluid engineering, such as forced convective cooling. In this study, we constructed a similarity law for the time variation of the surface temperature, assuming that the induced flow was heated by the discharge and that the dielectric was heated by the airflow. The similarity law was derived from the one-dimensional heat conduction equation in the dielectric, and the spatially averaged normalized temperature was then formulated as a function of the Biot and Fourier numbers. To experimentally validate the similarity law, the surface temperature, thrust, and power consumption were measured. The induced flow temperature and heat transfer coefficient were estimated based on the thrust and power consumption. The measured results verified that the similarity law was valid, regardless of the dielectric material, thickness, or applied voltage. This result supports the hypothesis regarding the heating mechanism in which the airflow is heated by Joule heating and the dielectric is heated by forced convection.