We derive a general expression for the thermal conductivity of simple fluids within a thermodynamic transport theory (TTT) in which the Onsager coefficients of an interacting system are related to those of an ideal reference system through the ratio of the determinants of the Hessians of the relevant thermodynamic potential. The transported quantity is identified with an effective energy density proportional to the rms energy fluctuations of a small fluid cell. The result expresses the thermal conductivity as the product of its dilute-gas value and a function of equilibrium thermodynamic properties, namely the specific heats at constant density and at constant ρ T and the temperature derivative of the latter, with no adjustable parameters. For hard spheres, it reduces to a previously verified expression in terms of the thermodynamic factor. The theory is tested against molecular dynamics results for the Lennard-Jones (LJ) and the truncated and shifted Lennard-Jones (LJTS) fluids in the supercritical region, for densities up to ρ^*=0.8, using equations of state based on perturbation theory. For the LJTS fluid, the mean absolute percentage error is below 8% for all the temperatures considered. For the LJ fluid, the predictions are compared with those of the revised Enskog theory for Mie fluids, using the same equation of state: TTT gives smaller errors at almost all temperatures, with a significant improvement at low temperatures, where the errors are reduced approximately by a factor between two and three.