The critical and phase behavior in the mass transport due to temperature gradients in binary liquid mixtures is theoretically examined. Hydrodynamic approach developed in our previous papers is used to calculate the dynamic parameters included in the mass transport equations. In hydrodynamic calculations, the cross- and thermodiffusion is related to the local temperature-induced pressure gradient in the liquid layer surrounding the selected molecule. The secondary macroscopic pressure gradient established in the system and the related barodiffusion is considered. The stationary concentration distribution in the mixture placed in temperature gradient is calculated. The phase diagram expressed as the temperature-concentration equilibrium curve, where the effective diffusion coefficient is zero, is build. At temperature below certain critical temperature, the resulting expression predicts the layering of liquid phases in a mixture. This critical temperature is expressed through the measurable interaction parameters of the mixture. At the critical temperature, the inflection point appears at the concentration distribution at the corresponding coordinate point. In the shifting into the depth of the two-phase domain (with decrease of temperature), this inflection is transformed into a jump in the concentration, which corresponds to the thermodynamically equilibrium concentrations of the components at the temperature at this jump point. The concentration distribution is calculated for critical and two-phase systems, and the prediction for the position of critical point and the interface boundary is obtained as the function of the temperature profile and the concentration. The theoretical results are in qualitative agreement with the available experimental data.