Thermal transport measurement has been an extremely powerful tool to explore the rich phases and hidden orders in various quantum materials. Recently, the discovery of the Kagome superconducting compound CsV₃Sb₅ provides a new platform to investigate the interplay between superconductivity, nematic phase, Dirac dispersion, and charge density wave (CDW) order. To understand the nature of these intertwined orders, we present a comprehensive study of the thermal conductivity as well as the thermal hall effect in the CsV₃Sb₅ single crystals. With the help of our self-developed differential amplifier and careful calibration, we measured the longitudinal and transverse thermal conductivity with high resolution in the precursor region of the superconducting state. The experimental methods, verification, and possible explanations will be discussed.