In this study, we developed a semi-active method to run a graphite calorimeter in the quasi-isothermal mode under high-energy x-ray beams. The rate of energy imparted by the beam during irradiation was compensated mainly by removing the electrical heating power based on the pre-calculation and in part by an active automated algorithm, as well, while the temperature of the calorimeter core was kept constant. Irradiations were performed under the linear electron accelerator x-ray beams at 6, 8, 10, 15, and 18 MV. A simple model was applied to analyze the results. The energy imparted to the core was determined with an uncertainty level of 0.2%-0.3%, and the results were reaffirmed by comparing it with that obtained by the quasi-adiabatic mode. The normalized root-mean-square deviation to the mean from the quasi-adiabatic mode was 0.11%, and the associated uncertainty was 0.16% taking into account the correlation of the uncertainty components. This level of agreement showed that the present method is practical for the high-energy x-ray dosimetry.