The Green-Kubo formalism, routinely used in combination with classical molecular dynamics for thermal conductivity calculations, is in this thesis extended for application in an ab initio DFT framework. An expression for the adiabatic energy flux from density-functional theory is derived and the resulting thermal conductivity is shown to be unaffected by the inherent ill-definedness of quantum mechanical energy densities and currents. The methodology is demonstrated by comparing results from ab-initio and classical molecular-dynamics simulations of a model liquid-Argon system, for which accurate inter-atomic potentials are derived by the force-matching method,and finally applied to compute the thermal conductivity of heavy water at ambient conditions.