The vacuum vessel of the KSTAR tokamak has a so large poloidal cross- section that workers can enter into the inside the vessel. To produce a clean plasma with low impurity concentrations it is planned that the whole vessel including plasma facing components will be baked out at $350^{circ}C$ and the base pressure of the vessel will be kept in the range of ultra high vacuum. Large thermal stresses are expected during bake-outs to a three-dimensionally complex structure of the vessel, consequent ununiformity of the temperature distribution and support systems to resist forces acting on the vessel. In this report variations of the thermal stress according to temperature gradients on the vessel and constraint conditions of supporting structures are studied and some possible counterplans are discussed.