The paper proposes an automated system for measuring the thermal conductivity of solids in the range from 5 to 400 W/(m·K) with increased accuracy and reduced duration of thermal conductivity measurement. The main element of this system is a thermal conductivity measuring transducer built on a bridge diagram balanced by heat flows. Using the theory of thermal circuits, the authors built a mathematical model of the measuring transducer. To implement the automated system for measuring thermal conductivity, materials of heat-conducting elements, reference specimens, and comparative elements were selected, and their design parameters were calculated. The setting parameters of the control system for balancing the bridge measuring diagram were determined. The authors also carried out the calibration of the developed thermal conductivity measuring system using reference specimens and obtained its calibration characteristic with a correlation coefficient R-square of 0.9987.