This thesis focuses on the study of the electronic thermal conductivity of the Thallium Calcium-Barium-Copper-Oxide (Tl2Ca2Ba2Cu3O10) superconductor by using the energy dispersion relation function, Boltzmann transport equation, and Bose-Einstein and Fermi-Dirac distribution functions. In addition, the electronic heat current density, the total energy, the electronic heat capacity, and the electronic thermal conductivity of the optically active phonon modes will be discussed. In a normal state of a Tl2Ca2Ba2Cu3O10 superconductor, the electronic heat capacity is directly proportional to the temperature, whereas, in a superconducting state, it is an exponentially decreasing curve. When it reaches critical temperature, it loses and is superconducting and converts into a normal conductor. The thermal conductivity of Tl2Ca2Ba2Cu3O10 in a normal state is directly proportional to the temperature, whereas, in a superconducting state, its graph is an exponentially increasing curve up to the critical temperature. When we consider the energy gap parameter, the dependency of electronic thermal conductivity on the temperature contains a term in addition to the linear T term. Keywords: Thallium-Calcium-Barium-Copper-Oxide, Normal State, Thermal Conductivity, Superconductivity