The new capabilities of the advanced two-channel AC calorimetry, when working at frequencies above quasi-static limit, were shown. The idea of the method was to use the information about the phases and the amplitudes of the temperature oscillations on both sides of a plate-like sample for direct simultaneous determination of the complex heat capacity Q(omega) and the complex thermal conductivity lambda(omega), when the thermal oscillations were measured on both sides of the sample. Therefore, the complete set of the complex thermal parameters can be measured in the same experiment. The method provides a possibility to answer the fundamental question about the value of imaginary part of the complex thermal conductivity. It was found, that the argument of the complex thermal conductivity is considerably small with respect to that of the complex heat capacity. Thus, at least within the error of the experiment the thermal conductivity at glass transition in glycerol can be considered as a real valued parameter. In spite of the strong frequency dependence of the complex heat capacity, no frequency dependency of the thermal conductivity was observed.