A simple and effective experimental approach has been developed and tested to study the temperature dependence of high-pressure methane sorption in moist organic-rich shales. This method, denoted as "multi-temperature" (short "multi-T") method, enables measuring multiple isotherms at varying temperatures in a single run. The measurement of individual sorption isotherms at different temperatures takes place in a closed system ensuring that the moisture content remains constant. The multi-T method was successfully tested for methane sorption on an organic-rich shale sample. Excess sorption isotherms for methane were measured at pressures of up to 25 MPa and at temperatures of 318.1 K, 338.1 K, and 348.1 K on dry and moisture-equilibrated samples. The measured isotherms were parameterized with a 3-parameter Langmuir-based excess sorption function, from which thermodynamic sorption parameters (enthalpy and entropy of adsorption) were obtained. Using these, we show that by taking explicitly into account water vapor as molecular species in the gas phase with temperature-dependent water vapor pressure during the experiment, more meaningful results are obtained with respect to thermodynamical considerations. The proposed method can be applied to any adsorbent system (coals, shales, industrial adsorbents) and any supercritical gas (e.g., CH4, CO2) and is particularly suitable for sorption measurements using the manometric (volumetric) method.