General expressions in terms of various square-bracket integrals for the thermal conductivity lambda and its first-order approximation [lambda](1) of a classical dilute binary gas mixture of nonspherical molecules have been obtained by extending the Taxman classical kinetic theory of transport phenomena within the framework of the Chapman-Enskog second approximation method for the mixture of spherical molecules. In the limit, [lambda](1) formula tends to the corresponding formula for a dilute simple gas of nonspherical molecules or a dilute binary gas mixture of spherical molecules. The dimensionalities of the square-bracket integrals belonging to [lambda](1) for the mixture of rigid spheroids having C-infinity v symmetry have been reduced by integrating analytically the velocity and angular velocity parts of the integrals. The resulting reduced quadratures are over the orientational coordinates of two colliding like or unlike spheroids. Two limiting checks are discussed which confirm that the quadrature formulas are correct.