Thermal gradients induce concentration gradients in alkali halide solutions, and the salt migrates towards hot or cold regions depending on the average temperature of the solution. This effect has been interpreted using the heat of transport, which provides a route to rationalize thermophoretic phenomena. Early theories provide estimates of the heat of transport at infinite dilution. These values are used to interpret thermodiffusion (Soret) and thermoelectric (Seebeck) effects. However, accessing heats of transport of individual ions at finite concentration remains an outstanding question both theoretically and experimentally. Here we discuss a computational approach to calculate heats of transport of aqueous solutions at finite concentrations, and apply our method to study lithium chloride solutions at concentrations >0.5 M. The heats of transport are significantly different for Li+ and Cl- ions, unlike what is expected at infinite dilution. We find theoretical evidence for the existence of minima in the Soret coefficient of LiCl, where the magnitude of the heat of transport is maximized. The Seebeck coefficient obtained from the ionic heats of transport varies significantly with temperature and concentration. We identify thermodynamic conditions leading to a maximization of the thermoelectric response of aqueous solutions.