The stability of the state of rest of a liquid medium in a gravitational field has been studied in a linear approximation. The density of the medium is linearly dependent on temperature and on the concentration of an admixture. In the background state, the admixture is distributed uniformly, and the temperature stratification is stable (the density decreases with altitude). Therefore, according to the known criteria, the state of rest is considered stable. It was shown that even relatively weak thermodiffusion at negative Soret coefficients can destabilize the stable density-stratified medium (neutral curves characterizing a monotonic instability in an infinite vertical layer were found). In the problem of heating by the side boundary, the possibility of an effective “negative heat capacity”—a decrease in the temperature in the heat input region—is shown.