Convective instabilities in side heated infinite vertical slots containing a single fluid are longitudinal, stationary, shear driven when the Prandtl number $Pr <12.5$ while they are oscillatory, buoyancy dominated with $Pr>12.5$ due to the diminished influence of the thermal diffusivity with increasing $Pr$. Here we examine the influence of the concentration field generated by thermodiffusion in a ternary mixture of otherwise uniform concentration on this phenomenon. We first derive expressions and calculate the basic steady one-dimensional flow taking into account the vertical concentration gradients caused by thermodiffusion. Linear stability of this basic state is performed and the critical Rayleigh number, wavenumber, frequency, and vertical concentration gradients are determined as functions of the two separation ratios, ratio of thermal expansivities, four Lewis numbers, and $Pr$. It is shown that the preferred instability remains longitudinal when the induced vertical stratification is stable while it is long transverse waves with unstable vertical stratification. These stability results are in agreement with those from an asymptotic model in the long wave approximation as well as when restricted to binary mixtures. The results are also in agreement with experiments with ternary mixture (Leahy-Dios et al., J. Chem. Phys., 2005) and binary mixtures (Bou-Ali et al. Physical Review E 1999, 2000). Stability restrictions on the operation of the thermogravitational column in both rectangular and annular geometries and supercritical nonlinear computations will be discussed.