We report an extensive analysis of the non-equilibrium response of alkali halide aqueous solutions (Na+/K+-Cl-) to thermal, gradients using state of the art non-equilibrium molecular dynamics simulations and thermal diffusion forced Rayleigh scattering experiments. The coupling between the thermal gradient and the resulting ionic salt mass flux is quantified through the Soret coefficient. We find the Soret Coefficient is of the order of 10(-3) K-1 for a wide range of concentrations., These relatively simple solutions feature a very rich behavior. The Soret coefficient decreases with concentration at high temperatures (higher than T similar to 315 K), whereas it increases, at lower temperatures. In agreement with previous experiments, we find evidence for sign inversion in, the Soret coefficient of NaCl and KCl solutions. We use an atomistic non-equilibrium molecular: dynamics approach to compute the Soret coefficients in a wide range of conditions and to attain further microscopic insight, On the heat transport mechanism, the behavior Of the Soret coefficient in aqueous solutions: The models employed in this work reproduce the Magnitude of the Soret coefficient, and the general dependence of this coefficient with temperature and salt concentration. We use the computer simulations as a microscopic approach to establish,a correlation between the sign and magnitude of the Soret, coefficients and ionic solvation and hydrogen bond structure of the solutions. Finally, we report an analysis of heat transport in ionic solution by quantifying the solution thermal conductivity as a function of concentration. The simulations accurately reproduce the decrease of the thermal conductivity with increasing salt concentration that is observed in experiments. An explanation of this behavior is provided.