The new capabilities of AC calorimetry, when working at frequencies above the classical (quasi-static) limit, were realized. The method of the Thermal-Waves-Transmission spectroscopy for simultaneous determination of the sample's heat capacity and thermal conductivity was developed on the basis of the advanced AC calorimetry technique. The idea of the method was to use the information about the phase and the amplitude of the thermal wave transmitted through a plate-like sample. The progress in the advanced technique was attained, when the thermal contact conductance was measured and taken into account. It was shown, that the Thermal-Waves-Transmission spectroscopy can be applied for various substances with thermal conductivity varied in the broad range 0.1-500 W/m K.