Results of the modified Rainwater-Friend theory for the initial density dependence of the thermal conductivity arising from the Lennard-Jones (12-6) potential in the range of reduced temperature 0.5 ≤ T*≤ 100 have been correlated. Informed by theory, a collection of 41 functional temperature terms was narrowed to the eight most significant terms by structural optimization. The new formulation is the first that extrapolates correctly beyond the data range to reduced temperatures of 0.01 and 150. It contributes significantly to an improved understanding of thermal conductivities of gases at low densities and low temperatures where measurements are rare.