TDS is not affected by all natural elements as some do not dissolve. Neon and Helium for exampleThat is conductivity which can be correlated to TDS imperfectly and is affected by temperature. We use it because it is a simple test and works well enough for our purposes. True TDS which would be measured by evaporated solids weight is not affected by temperature.
TDS is the concentration of solids in the water. It is not affected by temperature any more than any other mass or weight measurement.