The plasma actuator is an active flow control device utilizing the atmospheric dielectric barrier discharge. It has many advantages, and it is expected to be applied to a number of fluidic machines including enhancement of convection cooling. However, there is a significant problem when we apply the plasma actuator in the field of cooling, that is the actuator itself is a heat generation source due to the discharge. Although some research efforts have been devoted to understanding the heating characteristics of the plasma actuators, they made discussions only on the surface temperature, and any quantitative discussions on the amount of heating to the dielectric were not performed. The purpose of this study is to quantitatively discuss the heat transfer to the dielectric surface of the plasma actuator. For this purpose, the heat transfer coefficient and temperature of the wall-surface jet are estimated by applying it to a theoretical solution of the one-dimensional heat conduction inside the actuator. The time variation of temperature of the dielectric surface is measured using the IR camera. As a result, the estimation was reasonable near the electrode edge, but unphysical values were obtained downstream because of the small temperature rise and two-dimensional heat conduction in the dielectric. In the future, we need to analyze considering two-dimensional heat conduction utilizing numerical calculation.