It is easy to measure ionic conductivity of an aqueous solution by using a conductivity meter and selecting suitable conductivity probe. If by applying some mathematical relation it is possible to compute thermal conductivity it will be much easier.
I don't believe that a relationship exists between ionic conductivity of aqueous solutions and thermal conductivty, as least a general one. The mechanisms of conduction are indeed different, even if both are based on the mobility of the molecules. Just one example: the conductivity can be dramatically increased by introducing low amounts of either H3O+ or OH- ions. Because the ions are extremely small, their diffusion is excellent, hence the high ionic conductivity. But increasing or lowering the pH of water is not going to change significantly its thermal conductivity.
The electrical conductivity depends on the ions concentration and its mobilities. Thermal conductivity depends on diffusion of molecules of host material. Coefficients of diffusion have a slight connection with ion mobilities. But ion concentration have no connection with diffusion and, as a result, with thermal conductivity.
Thank you Dr. Korobeynikov for your nice explanation. Recently I have gone through a latest publication where a mathematical relation has been brought out between electrical conductivity and thermal conductivity. The relation is not applicable to ionic solution.