Steady-state bifurcation analysis is applied to a ternary-benzene-toluene xylene (BTX) dividing wall column (DWC) to synthesize robust temperature inferential controlled variables (CVs). The coupling between the prefractionator and the main column causes steady-state multiplicity in conventional tray temperature CV loops. Using physical insights into the DWC behavior, differential tray temperature across the side-draw and double differential temperature control across the prefractionator rectification section are shown to significantly mitigate the steady-state multiplicity. Control system variants (with and without prefractionator liquid split manipulation) with alternative temperature-based CVs exhibit nonlinear dynamic phenomena of seeking an infeasible temperature/purity set point and input multiplicity induced "wrong" control action leading to a low purity steady-state transition under closed loop operation. These nonlinear dynamic phenomena correlate with the bifurcation analysis results. The recommended control structure with robust temperature inferential CVs is shown to effectively reject very large feed composition changes, including for on-target product purity operation via temperature inferential CV update. The work brings out the importance of robust CV design for effective control of the highly coupled and nonlinear ternary DWC process.