Electrolyte solutions are essential in various physical, chemical, and biological processes. Thermal fields induce ion mass fluxes in electrolyte solutions, creating stable salt concentration gradients at stationary conditions. The response of the salt to the thermal field is quite complex, as the ions move towards hot or cold regions depending on the composition of the solution. While these phenomena are well-known, the microscopic mechanism determining thermodiffusion is still poorly understood. In this study, we used non-equilibrium molecular dynamics simulations and the Madrid 2019 forcefield to investigate the thermal transport properties of several electrolyte solutions: {Li+
, Na+
, K+
}Cl−
and {Li+
, Na+
, K+
}I−
. We show that the reduction of the thermal conductivity with salt concentration is correlated with the modification of the isothermal compressibility and the molar mass of the solution. We also calculate the Soret coefficient of the solutions and compare our results with those of existing experiments. The Madrid 2019 forcefield reproduces the main experimental trends of chloride solutions and the stronger thermophilic response of lithium salts. Our results suggest a connection between the ability of cations (Na+
, K+
) to disturb oxygen-oxygen correlations within the 0.35–0.5 nm inter-oxygen distance range and the thermophobicity of the solutions.